Communication system using shape-shifted sinusoidal waveforms

ABSTRACT

A data communication method in which input digital data is received and encoded into an encoded waveform having zero crossings representative of the input digital data. The encoding includes generating the encoded waveform based upon a continuous piecewise function having sinusoidal components. The continuous piecewise function may be used in generating a plurality of symbol waveforms, each of which occupies a period of the encoded waveform and represents bits of the input digital data. The plurality of symbol waveforms are defined so that a value of a phase offset used in the continuous piecewise function is different for each of the plurality of symbol waveforms, thereby resulting in each symbol waveform having a different zero crossing. An encoded analog waveform is generated from a representation of the encoded waveform and transmitted to a receiver.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.16/998,898, now U.S. Pat. No. 11,228,474, entitled HIGH SPECTRALEFFICIENCY DATA COMMUNICATIONS SYSTEM, filed Aug. 20, 2020, which is acontinuation of U.S. application Ser. No. 16/174,198, now U.S. Pat. No.10,791,014, entitled RECEIVER FOR HIGH SPECTRAL EFFICIENCY DATACOMMUNICATIONS SYSTEM USING ENCODED SINUSOIDAL WAVEFORMS, filed Oct. 29,2018, which claims the benefit of priority under 35 U.S.C. § 119(e) ofU.S. Provisional Patent Application No. 62/578,332, entitled DATACOMMUNICATIONS SYSTEM WITH HIGH SPECTRAL EFFICIENCY, filed on Oct. 27,2017, and of U.S. Provisional Patent Application No. 62/689,764,entitled HIGH SPECTRAL EFFICIENCY DATA COMMUNICATIONS SYSTEM USINGPERIODIC WAVEFORM MODULATION, filed on Jun. 25, 2018, the content ofeach of which is incorporated herein by reference in its entirety forall purposes.

FIELD

The present disclosure pertains generally to data communication systemsand, in particular, methods and systems for data communication basedupon sine wave modulation.

BACKGROUND

There are various transmission channels used for transmitting data orinformation. Telephone lines consisting of copper wires were used forwell over a hundred years for transmitting both voice and data. Radiotransmission of radio signals have been around for almost a hundredyears. A radio station sends a radio signal out over the airwaves to bereceived by a radio set. As is known, a radio station has programmingwhich may include music, news, or programs. Satellites are an example ofanother transmission channel in which a satellite dish positioned afirst location is used to transmit a signal to a satellite to be beamedor sent from the satellite to a second satellite dish positioned at alocation remote from the first location. More recently cellularcommunication systems have been used to communicate between cell phones.An enormous amount of data is being sent using cellular communicationsystems. At this point in time it is essential to be able to increasethe data throughput over any transmission channel that is used. It isalso important to address the problem of signal degradation duringtransmission of the signal. Some problems encountered when transmittinga signal over a transmission channel include transmission path delay,interference, and non-linearity.

Some transmission techniques or schemes that have been developed andused in an effort to increase data throughput over a transmissionchannel are Amplitude Modulation (AM), Frequency Modulation (FM), PhaseModulation, QAM (Quadrature Amplitude Modulation), QPSK (QuadraturePhase Shift Keying), PSK (Phase Shift Keying), and APSK (Amplitude andPhase Shift Keying).

Amplitude Modulation is a modulation technique used for transmittinginformation by use of a radio carrier wave. A sinusoidal carrier wavehas its amplitude modulated by an audio waveform before transmission.The audio waveform modifies the amplitude of the sinusoidal carrierwave. Some disadvantages associated with the use of an amplitudemodulation signal are that an amplitude modulation signal is notefficient in terms of its power usage, it is not efficient in terms ofits use of bandwidth, it requires a bandwidth equal to twice that of thehighest audio frequency, and it is prone to high levels of noise.

Frequency Modulation is a modulation technique that encodes informationin a carrier wave by varying the frequency of the wave. AlthoughFrequency Modulation has some advantages over Amplitude Modulation somedisadvantages include that it requires a more complicated demodulatorand that is has a poorer spectral efficiency than some other modulationtechniques.

QAM is a form of multilevel amplitude and phase modulation thatmodulates a source signal into an output waveform with varying amplitudeand phase. A system that employs QAM modulates a source signal into anoutput waveform with varying amplitude and phase. A message to betransmitted is mapped to a two-dimensional four quadrant signal space orconstellation having signal points or phasors each representing apossible transmission level. Each signal point in the constellation isreferred to as a symbol. The QAM constellation has a coordinate systemdefined by an I or in-phase axis and a Q or quadrature axis or an IQplane. A symbol may be represented by both I and Q components. One ofthe disadvantages of the use of QAM is that for the higher data ratesthe peak to average power ratio is high. For example, in a typicalconstellation diagram for 16QAM, it can be seen that there are fourpossible power levels. As the order of the modulation increases, so thenumber of power levels needed increases. All of this results in everhigher peak to average power ratios being experienced.

QPSK has a synchronous data stream modulated onto a carrier frequencybefore being over a channel. The carrier can have four states such as45°, 135°, 225°, or 315°. QPSK also employs a quadrature modulationwhere the signal points can be described using two orthogonal coordinateaxes, such as the IQ plane. With conventional QPSK, there is the problemthat the transition between two diagonal transmission symbol points inthe complex plane passes through the zero point. In the transitionbetween these diagonal transmission symbols, a lowering of the amplitudemay occur, the so-called envelope, to practically zero. On the receiverside, it complicates the necessary synchronization and favorsnonlinearities in the transmission path, signal distortion, and unwantedintermodulation.

PSK is another digital modulation process which transmits a message bymodulating the phase of a carrier wave. One disadvantage of using PSK isthat when a high order PSK constellation is used the error-rate becomestoo high.

As the name APSK indicates, this form of modulation uses amplitude andphase shift keying. In this modulation scheme a signal is conveyed bymodulating both the amplitude and the phase of a carrier wave Amplitudeand frequency shift keying is able to reduce the number of power levelsrequired to transmit information for any given modulation order.

SUMMARY

In one aspect the disclosure relates to a method for periodic waveformmodulation. The method includes receiving input digital data andencoding the input digital data at selected phase angles Θ₁, Θ₂, Θ₃, Θ₄of an unmodulated sinusoidal waveform in order to create a modulatedsinusoidal waveform. The encoding process includes selectively reducinga power of the unmodulated sinusoidal waveform at ones of the selectedphase angles Θ₁, Θ₂, Θ₃, Θ₄ in accordance with bit values of the inputdigital data so as to respectively define first, second, third andfourth data notches in the modulated sinusoidal waveform. An encodedanalog waveform is then generated, using a digital-to-analog converter,from a digital representation of the modulated sinusoidal waveform. Thedata notches are formed such that a first energy corresponding to afirst cumulative power difference between a power of the modulatedsinusoidal waveform and a power of the unmodulated sinusoidal waveformover a first phase angle range subtended by the first data notch issubstantially equal to a third energy corresponding to a thirdcumulative power difference between the power of the modulatedsinusoidal waveform and the power of the unmodulated sinusoidal waveformover a third phase angle range subtended by the third data notch. Thedata notches are also formed such that a second energy corresponding toa second cumulative power difference between the power of the modulatedsinusoidal waveform and the power of the unmodulated sinusoidal waveformover a second phase angle range subtended by the second data notch issubstantially equal to a fourth energy corresponding to a fourthcumulative power difference between the power of the modulatedsinusoidal waveform and the power of the unmodulated sinusoidal waveformover a fourth phase angle range subtended by the fourth data notch.

In one embodiment the phase angle Θ₃ is equal to the sum of the phaseangle Θ₁ and 180° and the phase angle Θ₄ is equal to the sum of thephase angle Θ₂ and 180°. In another embodiment the phase angle Θ₁ isbetween 44.5° and 45.5°, the phase angle Θ₂ is between 134.5° and135.5°, the phase angle Θ₃ is between 224.5° to 225.5°, and the phaseangle Θ₄ is between 314.5° to 315.5°.

In one embodiment the first data notch is representative of a first bitvalue of the bit values and the second data notch is representative of asecond bit value of the bit values. In one implementation a minimumamplitude of the first data notch is a first percentage of the amplitudeof the unmodulated sinusoidal waveform at the phase angle Θ₁ and aminimum amplitude of the second data notch is a second percentage of theamplitude of the unmodulated sinusoidal waveform at the phase angle Θ₂,the first percentage being different from the second percentage. Whenthe first data notch is representative of a first plurality of the bitvalues it may include a first plurality of transition featuresrespectively representative of the first plurality of the bit values. Inthis case the third data notch may be representative of a secondplurality of the bit values and may include second plurality oftransition features respectively representative of the second pluralityof the bit values.

In a carrier-stacked implementation the unmodulated sinusoidal waveformis of a first frequency and additional input digital data is encoded atones of the selected phase angles Θ₁, Θ₂, Θ₃, Θ₄ of an additionalunmodulated sinusoidal waveform of a second frequency to create anadditional modulated sinusoidal waveform. The encoding process includesselectively reducing a power of the additional unmodulated sinusoidalwaveform at ones of the selected phase angles Θ₁, Θ₂, Θ₃, Θ₄ inaccordance with bit values of the additional input digital data so as torespectively define additional first, second, third and fourth datanotches in the additional modulated sinusoidal waveform. An additionalencoded analog waveform is generated, using a digital-to-analogconverter, from a digital representation of the additional modulatedsinusoidal waveform. In this case an additional first cumulative powerdifference between a power of the additional modulated sinusoidalwaveform and a power of the additional unmodulated sinusoidal waveformover an additional first phase angle range subtended by the additionalfirst data notch is substantially equal to an additional thirdcumulative power difference between the power of the additionalmodulated sinusoidal waveform and the power of the additionalunmodulated sinusoidal waveform over an additional third phase anglerange subtended by the additional third data notch. Similarly, anadditional second cumulative power difference between the power of theadditional modulated sinusoidal waveform and the power of the additionalunmodulated sinusoidal waveform over an additional second phase anglerange subtended by the additional second data notch is substantiallyequal to an additional fourth cumulative power difference between thepower of the additional modulated sinusoidal waveform and the power ofthe additional unmodulated sinusoidal waveform over an additional fourthphase angle range subtended by the additional fourth data notch.

In one embodiment the power of the unmodulated sinusoidal waveform isreduced in accordance with the bit values of the input digital data onlyat the phase angles Θ₁ and Θ₃. In this case the power of the unmodulatedsinusoidal waveform may be reduced for purposes of energy balancing atthe phase angles Θ₂ and Θ₄ independent of the input digital data.

The disclosure also pertains to a modulation method using carrierstacking which involves receiving input digital data and encoding theinput digital data at selected phase angles of a plurality of sinusoidalwaveforms so as to create a plurality of modulated sinusoidal waveforms.The method further includes generating an output analog waveformincluding a plurality of encoded analog communication signalscorresponding to a plurality of digital representations of the pluralityof modulated sinusoidal waveforms. In this case adjacent modulatedsinusoidal waveforms are separated in frequency by less than 15 Hz andany sideband included within the output analog waveform is of a power atleast 50 dB below a power of the encoded analog communication signalassociated with the sideband.

The encoding process may include encoding the input digital data atphase angles Θ₁, Θ₂, Θ₃, Θ₄ of an unmodulated sinusoidal waveform tocreate a first modulated sinusoidal waveform by selectively reducing apower of the unmodulated sinusoidal waveform at ones of the phase anglesΘ₁, Θ₂, Θ₃, Θ₄ in accordance with bit values of the input digital data,thereby respectively defining first, second, third and fourth datanotches in the first modulated sinusoidal waveform. In this case a firstcumulative power difference between a power of the first modulatedsinusoidal waveform and a power of the unmodulated sinusoidal waveformover a first phase angle range subtended by the first data notch issubstantially equal to a third cumulative power difference between thepower of the first modulated sinusoidal waveform and the power of theunmodulated sinusoidal waveform over a third phase angle range subtendedby the third data notch. In addition, a second cumulative powerdifference between the power of the first modulated sinusoidal waveformand the power of the unmodulated sinusoidal waveform over a second phaseangle range subtended by the second data notch is substantially equal toa fourth cumulative power difference between the power of the firstmodulated sinusoidal waveform and the power of the unmodulatedsinusoidal waveform over a fourth phase angle range subtended by thefourth data notch.

The subtraction process may include detecting zero crossings of thedigital values representing the modulated sinusoidal waveform. In oneembodiment the method includes detecting a preamble within the receiveddigital data sequence.

The disclosure is further directed to a data communication method. Themethod includes receiving input digital data and encoding the inputdigital data using a plurality of symbol waveforms. Each of theplurality of symbol waveforms occupies a period of a composite encodedwaveform and represents one or more bits of the input digital data. Eachsymbol waveform of the plurality of symbol waveforms has a positiveelliptical segment and a negative elliptical segment. In addition, eachsymbol waveform is defined so that (i) a zero crossing from the positiveelliptical segment to the negative elliptical segment of the symbolwaveform is different for each of the plurality of symbol waveforms, and(ii) an energy of the positive elliptical segment of the symbol waveformis substantially equal to an energy of the negative elliptical segmentof the symbol waveform. The method further includes generating, using adigital-to-analog converter, an encoded analog waveform from a digitalrepresentation of the composite encoded waveform.

In yet another aspect, the disclosure relates to a method of recoveringinformation encoded by symbol waveforms wherein each of the symbolwaveforms occupies a period of an encoded composite waveform andincludes a positive elliptical segment and a negative elliptical segmentof substantially equal energy. The method includes receiving an encodedanalog waveform generated using the symbol waveforms and generatingdigital symbol samples representing the symbol waveforms. The methodfurther includes identifying a first sample of the digital symbolsamples corresponding to a transition from ones of the digital signalsamples having negative values to ones of the digital signal sampleshaving positive values. The method also includes determining a secondsample of the digital signal samples corresponding to a transition fromother ones of the digital signal samples having positive values to otherones of the digital signal samples having negative values. The second ofthe digital samples defines a transition from the positive ellipticalsegment of one of the symbol waveforms to the negative ellipticalsegment of the one of the symbol waveforms. The input digital data isthen estimated based upon at least the first sample and the secondsample.

The disclosure also relates to a system including an input bufferconfigured to store input digital data and a time domain modulator forencoding the input digital data using a plurality of symbol waveforms.The time domain modulator is configured to effect the encoding so thateach of the plurality of symbol waveforms occupies a period of acomposite encoded waveform and represents one or more bits of the inputdigital data. Each symbol waveform of the plurality of symbol waveformshas a positive elliptical segment and a negative elliptical segment. Thetime domain modulator is further configured to define each symbolwaveform so that (i) a zero crossing from the positive ellipticalsegment to the negative elliptical segment of the symbol waveform isdifferent for each of the plurality of symbol waveforms, and (ii) anenergy of the positive elliptical segment of the symbol waveform issubstantially equal to an energy of the negative elliptical segment ofthe symbol waveform. The system also includes one or moredigital-to-analog converters for generating an encoded analog waveformfrom a digital representation of the composite encoded waveform.

In another aspect, the disclosure pertains to a method which involvesreceiving input digital data and encoding the input digital data in awaveform wherein one or more bit values of the input digital data areencoded within each period of the waveform. The method includesgenerating, using a digital-to-analog converter, an encoded analogwaveform from a digital representation of the periodic waveform whereinthe encoded analog waveform is of a frequency f and a power P. Themethod is further characterized in that any signal of frequency f′resulting from the encoding is of a power P′ at least 50 dB less thanpower P, where f′ is offset from f by more than 25 Hz.

The encoding operation may include modulating a sinusoidal waveform atselected phase angles within a period of the sinusoidal waveform. Inaddition, the modulating may include selectively reducing a power of thesinusoidal waveform at ones of the selected phase angles in accordancewith the one or more bit values of the input digital data. Themodulating may further include selectively reducing a power of thesinusoidal waveform at a first phase angle of the selected phase anglesand a second phase angle of the selected phase angles accordance withthe one or more bit values of the input digital data wherein the firstphase angle and the second phase angle are separated by approximately180 degrees.

The disclosure is further directed to a system including an input bufferfor storing input digital data and a sub-periodic modulator for encodingthe input digital data in a waveform. The sub-periodic modulator isoperative to encode one or more bit values of the input digital datawithin each period of the waveform. The system further includes one ormore digital-to-analog converters for generating an encoded analogwaveform from a digital representation of the periodic waveform whereinthe encoded analog waveform is of a frequency f and a power P. Themodulator is configured to effect the encoding such that any signal offrequency f′ resulting from the encoding is of a power P′ at least 50 dBless than power P, where f′ is offset from f by more than 25 Hz.

In yet another aspect the disclosure relates to a method which includesreceiving input digital data and encoding the input digital data in asinusoidal waveform. The encoding is performed by modulating thesinusoidal waveform at selected phase angles within a period of thesinusoidal waveform, thereby creating a modulated sinusoidal waveform.The method further includes generating, using a digital-to-analogconverter, an encoded analog waveform from a digital representation ofthe modulated sinusoidal waveform. The modulating includes forming afirst data notch at a first phase angle of the selected phase angleswherein the first data notch includes a first plurality of transitionfeatures and subtends a first phase angle range about the first phaseangle, the first plurality of transition features being representativeof a first plurality of bit values included within the input digitaldata.

The disclosure is further directed to a system including an input bufferfor storing input digital data and a sub-periodic modulator for encodingthe input digital data in a sinusoidal waveform. The sub-periodicmodulator is configured to perform the encoding by modulating thesinusoidal waveform at selected phase angles within a period of thesinusoidal waveform, thereby creating a modulated sinusoidal waveform.The system also includes one or more digital-to-analog converters forgenerating an encoded analog waveform from a digital representation ofthe modulated sinusoidal waveform. The sub-periodic modulator isconfigured to form a first data notch at a first phase angle of theselected phase angles wherein the first data notch includes a firstplurality of transition features and subtends a first phase angle rangeabout the first phase angle, the first plurality of transition featuresbeing representative of a first plurality of bit values included withinthe input digital data.

In another form of the present disclosure, a data communication systemis disclosed which comprises a transmitter for receiving a symbol andfor generating a modulated sinusoidal waveform representative of thesymbol, circuitry for transmitting the modulated sinusoidal waveform, areceiver for receiving the modulated sinusoidal waveform, and circuitryfor converting the modulated sinusoidal waveform into the symbol.

In yet another form of the present disclosure, a data communicationssystem is disclosed which comprises a transmitter for receiving a symboland for generating a modulated sinusoidal waveform representative of thesymbol, the modulated sinusoidal waveform having a first layer ofmodulation and a second layer of modulation, circuitry for transmittingthe modulated sinusoidal waveform, a receiver for receiving themodulated sinusoidal waveform, and circuitry for converting themodulated sinusoidal waveform into the symbol.

In still another form of the present disclosure, a data communicationssystem is disclosed which comprises a transmitter for receiving data andfor generating a modulated sinusoidal waveform representative of thedata, the modulated sinusoidal waveform having an amplitude with themodulated sinusoidal waveform having a first modulation at a firstfrequency with the first modulation being a reduction in the power ofthe modulated sinusoidal waveform at the first frequency, and circuitryfor transmitting the modulated sinusoidal waveform, and a receiver forreceiving the modulated sinusoidal waveform, and circuitry forconverting the modulated sinusoidal waveform into the symbol.

The present disclosure further provides a data communications systemwith high spectral efficiency that is capable of transmitting a largeamount of data over a channel by providing a modulated sinusoidalwaveform.

The present disclosure is also directed to a data communications systemthat provides a sinusoidal waveform that carries informationsub-periodic with each sinusoidal wave capable of transporting 2, 4, ormore symbols, such as 20 bits per period.

The present disclosure further provides a data communications system inwhich the amount of information transported is a function of the carrierfrequency and modulation points within the period, not the spectrumused.

The present disclosure is also directed to a data communications systemin which single or multiple layers of amplitude reductions can be usedto increase throughput.

The present disclosure is related to a data communication system inwhich a modulated sinusoidal waveform is produced having a large ofamount of information.

The present disclosure is also directed to a data communication systemin which a modulated sinusoidal waveform representative of a signal isproduced and transmitted to a receiver in which the receiver is capableof reconstructing the signal from the modulated sinusoidal waveform.

The present disclosure also pertains to a data communication method inwhich input digital data is received and encoded into a shape-shiftedsinusoidal encoded waveform having zero crossings representative of theinput digital data. The encoding includes generating the encodedwaveform based upon a continuous piecewise function having sinusoidalcomponents. The continuous piecewise function may be used in generatinga plurality of symbol waveforms, each of which occupies a period of theencoded waveform and represents bits of the input digital data. Theplurality of symbol waveforms are defined so that a value of a phaseoffset used in the continuous piecewise function is different for eachof the plurality of symbol waveforms, thereby resulting in each symbolwaveform having a different zero crossing. An encoded analog waveform isgenerated from a representation of the encoded waveform and transmittedto a receiver.

In a further aspect the disclosure relates to a data communicationmethod in which input digital data is received and encoded into ashape-shifted sinusoidal encoded waveform having zero crossingsrepresentative of the input digital data. The encoding includesgenerating each period of the encoded waveform using a continuouspiecewise function having the form:

${Y(\theta)} = \begin{pmatrix}{\sin(\theta)} & {{{{0 \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < a} \\{f(\theta)} & {{{{a \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < b} \\{g(\theta)} & {{{{b \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < c} \\{\sin(\theta)} & {c \leq \theta}\end{pmatrix}$

where Y is a value of the encoded waveform, θ represents angulardisplacement, and where:

f(x)=sin(π*(θ−d)/(π−2d)),

g(x)=sin(π*(θ+3d)/(π+2d)),

a=π/2,

b=π−d,

c=3π/2,

wherein d represents a phase shift. The method includes generating anencoded analog waveform from a representation of the encoded waveform.

In another aspect the disclosure describes a method of recovering inputdigital data encoded by symbol waveforms where each of the symbolwaveforms occupies a period of a shape-shifted sinusoidal encodedwaveform. Each period of the encoded waveform from which the inputdigital data is recovered is generated using a continuous piecewisefunction having the form:

${Y(\theta)} = \begin{pmatrix}{\sin(\theta)} & {{{{0 \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < a} \\{f(\theta)} & {{{{a \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < b} \\{g(\theta)} & {{{{b \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < c} \\{\sin(\theta)} & {c \leq \theta}\end{pmatrix}$

where Y is a value of the encoded waveform, θ represents angulardisplacement, and where:

f(x)=sin(π*(θ−d)/(π−2d)),

g(x)=sin(π*(θ+3d)/(π+2d)),

a=π/2,

b=π−d,

c=3π/2,

wherein d represents a phase shift. The method includes receiving anencoded analog waveform generated using the encoded waveform. Digitalsymbol samples representing the symbol waveforms included within theencoded waveform are generated. A first sample of the digital symbolsamples corresponding to a transition in polarity of the digital symbolsamples from a first polarity to a second polarity is then identified.The method includes determining a second sample of the digital signalsamples corresponding to a transition from other ones of the digitalsignal samples of the second polarity to other ones of the digitalsignal samples of the first polarity. The input digital data is thenestimated based upon the first sample and the second sample.

In yet a further aspect the disclosure relates to a system including aninput buffer configured to store input digital data. The system includesa time domain modulator for encoding the input digital data into ashape-shifted sinusoidal encoded waveform having zero crossingsrepresentative of the input digital data. The time domain modulatorgenerates each period of the encoded waveform using a continuouspiecewise function having the form:

${Y(\theta)} = \begin{pmatrix}{\sin(\theta)} & {{{{0 \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < a} \\{f(\theta)} & {{{{a \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < b} \\{g(\theta)} & {{{{b \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < c} \\{\sin(\theta)} & {c \leq \theta}\end{pmatrix}$

where Y is a value of the encoded waveform, θ represents angulardisplacement, and where:

f(x)=sin(π*(θ−d)/(π−2d)),

g(x)=sin(π*(θ+3d)/(π+2d)),

a=π/2,

b=π−d,

c=3π/2,

wherein d represents a phase shift. The system includes one or moredigital-to-analog converters for generating an encoded analog waveformfrom a representation of the encoded waveform.

The disclosure also relates to a data communication method in whichinput digital data is received and encoded into a shape-shiftedsinusoidal encoded waveform having zero crossings representative of theinput digital data. The encoding includes generating each period of theencoded waveform using a continuous function y(θ), where y(θ) given by:

y(θ)=sin(θ−a(1−cos(θ)))

where

a=½πs·sec(πs/2)²

wherein s represents a phase shift. The method includes generating anencoded analog waveform from a representation of the encoded waveform.

In another aspect the disclosure describes a method of recovering inputdigital data encoded by symbol waveforms where each of the symbolwaveforms occupies a period of a shape-shifted sinusoidal encodedwaveform. Each period of the encoded waveform from which the inputdigital data is recovered is generated using a continuous function y(θ),where y(θ) given by:

y(θ)=sin(θ−a(1−cos(θ)))

where

a=½πs·sec(πs/2)²

wherein s represents a phase shift. The method includes receiving anencoded analog waveform generated using the encoded waveform. Digitalsymbol samples representing the symbol waveforms included within theencoded waveform are generated. A first sample of the digital symbolsamples corresponding to a transition in polarity of the digital symbolsamples from a first polarity to a second polarity is then identified.The method includes determining a second sample of the digital signalsamples corresponding to a transition from other ones of the digitalsignal samples of the second polarity to other ones of the digitalsignal samples of the first polarity. The input digital data is thenestimated based upon the first sample and the second sample.

The disclosure is also concerned with a system including an input bufferconfigured to store input digital data. The system includes a timedomain modulator for encoding the input digital data into ashape-shifted sinusoidal encoded waveform having zero crossingsrepresentative of the input digital data. The time domain modulatorgenerates each period of the encoded waveform using a continuousfunction y(θ), where y(θ) given by:

y(θ)=sin(θ−a(1−cos(θ)))

where

a=½πs·sec(πs/2)²

wherein s represents a phase shift. The system includes one or moredigital-to-analog converters for generating an encoded analog waveformfrom a representation of the encoded waveform.

The disclosure further relates to a data communication method whichincludes receiving input digital data and encoding the input digitaldata into an encoded waveform representative of the input digital data.The encoded waveform is of a wavelength λ and each period of the encodedwaveform includes a first half sinusoid corresponding to one half of afirst sinusoid of wavelength λ₁ and a second half sinusoid correspondingto one half of a second sinusoid of wavelength λ₂, where λ₁+λ₂=λ. Theencoding includes generating each period of the encoded waveform so asto represent one bit of the input digital data. The first half sinusoidis of a first polarity and the second half sinusoid is of a secondpolarity opposite to the first polarity. A first bit value of the inputdigital data is represented by a period of the encoded waveform when λ₁is greater than λ₂ and a second bit value of the input digital data isrepresented by a period of the encoded waveform when λ₂ is greater thanλ₁. An encoded analog waveform is then generated from a digitalrepresentation of the encoded waveform.

Each period of the encoded waveform may be represented by a functionT(t), where T(t) is given by:

${T(t)} = \left\{ {{\begin{matrix}{{{{{{\sin\left( \frac{2{\pi t}}{\lambda_{1}} \right)}0} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < c} \\{{{{{{- {\sin\left( \frac{2{\pi\left( {t - c} \right)}}{\lambda_{2}} \right)}}c} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < \lambda}\end{matrix}{where}c} = {{\frac{\lambda}{2}\left( {1 + u} \right)u} = {{\left( {{2b} - 1} \right)s\lambda_{1}} = {{{\lambda\left( {1 + u} \right)}\lambda_{2}} = {\lambda\left( {1 - u} \right)}}}}} \right.$

wherein b represents a value of the input digital data being encoded, cis a root location joining the first half sinusoid and the second halfsinusoid, and s represents a change between the root location and adefault root location corresponding to λ₁=λ₂.

In a further aspect the disclosure pertains to a method of recoveringinput digital data encoded into an encoded waveform of a wavelength λwherein each period of the encoded waveform includes a first halfsinusoid corresponding to one half of a first sinusoid of wavelength λ₁and a second half sinusoid corresponding to one half of a secondsinusoid of wavelength λ₂, where λ₁+λ₂=λ. The encoding includesgenerating each period of the encoded waveform so as to represent onebit of the input digital data where the first half sinusoid is of afirst polarity and the second half sinusoid is of a second polarityopposite to the first polarity. A first bit value of the input digitaldata is represented when L is greater than L and a second bit value ofthe input digital data is represented when L is greater than L. Themethod includes receiving an encoded analog waveform generated using theencoded waveform. Pursuant to the method, digital symbol samples aregenerated from the received waveform and represent the first halfsinusoid and the second half sinusoid of a first period of the encodedwaveform. The method includes computing a first sum of squares of thedigital symbol samples over a first integration interval encompassed bythe first half sinusoid and computing a second sum of squares of thedigital symbol samples over a second integration interval encompassed bythe second half sinusoid. The method further includes estimating a bitof the input digital data encoded by a first period of the encodedwaveform based upon a comparison of the first sum of squares and thesecond sum of squares.

These and other advantages of the present disclosure will becomeapparent after considering the following detailed specification inconjunction with the accompanying drawings, wherein:

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. Also, common but well-understood elements that are useful ornecessary in a commercially feasible embodiment are often not depictedin order to facilitate a less obstructed view of these variousembodiments of the present invention. In the drawings, like referencecharacters generally refer to like features (e.g., functionally similarand/or structurally similar elements).

FIG. 1 is a block diagram of a communications system having atransmitter and a receiver constructed in accordance with the presentdisclosure.

FIG. 2 is a block diagram of an embodiment of the transmitter shown inFIG. 1.

FIG. 3 is a block diagram of an embodiment of the receiver shown in FIG.1.

FIG. 4 is a waveform diagram of a modulated sinusoidal waveform that isemployed by use of the communication system shown in FIG. 1.

FIG. 5 is a table of notch angles and amplitudes of the modulatedsinusoidal waveform shown in FIG. 4.

FIGS. 6-9 illustrate exemplary modulation perturbations which eachdefine a plurality of step transitions for encoding multiple data bits.

FIG. 10 is a waveform diagram of a modulated sinusoidal waveformrepresenting the letter H; and

FIG. 11 is a waveform diagram of a modulated sinusoidal waveformrepresenting the word HELLO.

FIGS. 12A and 12B illustrate application of the inventiveenergy-balancing principle to the case in which each modulationperturbation is representative of a single data bit.

FIG. 13 is an IQ diagram for an energy-balanced modulated sine wave inwhich each modulation perturbation is representative of five data bits.

FIG. 14 is a block diagram of an energy-balancing coder/modulator inaccordance with the disclosure.

FIG. 15 is a block diagram of a receiver configured to demodulate anddecode a modulated sine wave generated by the coder/modulator of FIG.15.

FIG. 16 is a functional block diagram of an embodiment of anenergy-balancing transmitter suitable for implementation using a fieldprogrammable gate array (FPGA).

FIG. 17 is a flowchart representative of an exemplary sequence ofencoding and other operations performed by an energy balancingtransmitter in accordance with an embodiment.

FIG. 18, which is a functional block diagram of an another embodiment ofan energy-balancing transmitter suitable in accordance with thedisclosure.

FIG. 19 is a flowchart representative of an exemplary sequence ofencoding and other operations performed by the energy balancingtransmitter in accordance with an embodiment.

FIG. 20 is a block diagram representation of a multi-carrierenergy-balancing transmitter in accordance with an embodiment.

FIG. 21 is a functional block diagram of a receiver configured toreceive and demodulate encoded sine waves transmitted by anenergy-balancing transmitter configured in accordance with thedisclosure.

FIG. 22 is a functional block diagram of an embodiment of anenergy-balancing transmitter configured to generate and transmitsinusoidal waveforms modulated with multi-bit features at selected phaseangles.

FIG. 23 is a functional block diagram of an another embodiment of anenergy-balancing transmitter configured to generate and transmitsinusoidal waveforms modulated with multi-bit features at selected phaseangles.

FIG. 24 illustrates an area bounded by an unmodulated sinusoid and amulti-bit data notch.

FIG. 25 is a screenshot generated by a spectrum analyzer when providedwith an encoded sinusoid modulated with data notches at 45°, 135°, 225°and 315°.

FIGS. 26A-26C illustrate various alternate data encoding schemes inaccordance with the disclosure.

FIGS. 27A and 27B illustrate sinusoids encoded in an energy-balancedmanner using data notches of alternative shapes.

FIG. 28 illustrates elliptical waveforms encoded in an energy-balancedmanner in accordance with the disclosure.

FIG. 29 is a functional block diagram of an embodiment of anenergy-balancing transmitter configured to generate and transmitzero-crossing-phase-modulated elliptical waveforms of the typeillustrated in FIG. 28.

FIG. 30 is a functional block diagram of a receiver configured toreceive and demodulate zero-crossing-phase-modulated ellipticalwaveforms.

FIGS. 31A and 31B illustrate shape-shifted sinusoidal waveformsrespectively encoded using a continuous piecewise function and analternate continuous function.

FIG. 32 is a functional block diagram of an embodiment of a transmitterconfigured to generate and transmit shape-shifted sinusoidal waveformsof the type illustrated in FIG. 31.

FIG. 33 is a functional block diagram of an embodiment of a receiverconfigured to receive and demodulate shape-shifted sinusoidal continuouspiecewise waveforms transmitted by a transmitter.

FIGS. 34A and 34B illustrate shape-shifted sinusoidal waveforms producedby a transmitter configured and in accordance with the disclosure.

FIG. 35 illustrates an exemplary process for decoding information withina received shape-shifted shifted sinusoid encoded in accordance with thedisclosure.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like numbers refer to like items,number 10 identifies a communications system constructed according tothe present disclosure. With reference now to FIG. 1, the datatransmission or communications system 10 is shown to comprise atransmitter 12 for receiving a symbol 14 and for generating a modulatedsinusoidal waveform 16 representative of the symbol 14, and circuitry 18for transmitting the modulated sinusoidal waveform 16 over acommunications channel 20. The system 10 also comprises a receiver 22for receiving the modulated sinusoidal waveform 16, and circuitry 24 forconverting the modulated sinusoidal waveform into the symbol 14. Thecommunications channel 20 may be provided by media such as coaxialcable, fiber optic cable, telephone or telephone company (telco) linessuch as copper wires, open air as by radio frequency or space orsatellite. The channel 20 may carry one or many messages. The system 10will have input data, such as the symbol 14, perform some form ofprocessing of the input data within the transmitter 12 and then transmitthe processed data as the signal 16 over the communications channel 20.The receiver 22 is capable of receiving the signal 16 and thenperforming a converse operation or process to recover the input data orsymbol 14 to output the input data or symbol 14 to some other device,such as, by way of example only, a monitor, a computer, an audiocomponent, or a speaker.

With reference now to FIG. 2, a block diagram of the transmitter 12 isdepicted. The transmitter 12 has a microcontroller 30 that has an USBinput 32 for receiving the symbol 14 or other input data such as music,video, text, or a combination thereof. The symbol 14 is provided fromthe USB input 32 to the microcontroller 30 over a connection 34. Themicrocontroller 30 may also include memory 36, such as a 16 MB memory,an 8 MHz input 38, and a digital-to-analog converter (DAC) output 40.The microcontroller 30 can produce a sine wave or other waveform and asine table, read in the symbol 14, disassemble the symbol 14, and inserta modulation perturbation or notch in the sine wave or a sinusoidal waveto generate the modulated sinusoidal waveform 16 representative of thesymbol 14. The sinusoidal wave may have the modulation perturbationinserted at phase angles of 45°, 135°, 225°, and 315°. As will beexplained more fully herein, the inserted modulation perturbation mayrepresent a bit of information. The microcontroller 30 provides thesignal 16 to the DAC output 40. The DAC output 40 may be connected toother circuitry (not shown) that can transmit the signal 16. An exampleof the microcontroller 30 is a device manufactured by STMicroelectronicsknown as STM32F756 family of microcontrollers or other similarmicrocontroller may be used.

FIG. 3 shows a block diagram of the receiver 22 constructed according tothe present disclosure. The receiver 22 comprises a microcontroller 42that has an analog to digital converter (ADC) input 44 for receiving thesignal 16 transmitted by the transmitter 12. The signal 16 from theinput 44 is provided to the microcontroller 30 over a connection 46. Themicrocontroller 42 may also include memory 48, such as a 16 MB memory,an 8 MHz input 50, and an RS232 or USB output 52. The output 52 isprovided to another device (not shown), such as a speaker. Themicrocontroller 42 is capable of generating a sine wave and a sinetable. The microcontroller 42 also reads in the signal 16 from the ADCinput 44, reassembles the symbol 14, and sends the symbol to the output52 for use by the other device (not shown). Again, an example of themicrocontroller 30 is a device manufactured by STMicroelectronics knownas STM32F756 family of microcontrollers or other similar microcontrollermay be used.

Modulation is commonly understood to be variation of amplitude,frequency, or phase of a carrier wave. The following discloses a newform of modulation that is used by the system 10. This new form ofmodulation inserts a disturbance, perturbation or notch in a wave suchas a sinusoidal wave at multiple phase angles during each period of thewave. The inserted notch has a frequency that is a multiple of the wavefrequency. This form of modulation may be termed periodic sine wavemodulation. In embodiments in which modulation perturbations of the sametype are used at the same phase angles during each wave period, themodulation may be referred to as sub-periodic or intra-periodic sinewave modulation.

FIG. 4 illustrates an example of one period of a modulated sine wave 100having a set of four modulation perturbations in the form of notches. Asshown, the modulated sine wave 100 corresponds to a sinusoidal wave thatis disturbed at a frequency (e.g., 4 times per sine wave period) that isa multiple of the sine wave frequency. In this particular case, thesinusoidal wave is disturbed four times at phase angles of 45°, 135°,225°, and 315° in order to create a set of four modulationperturbations. As may be appreciated from FIG. 4, the sinusoidalwaveform 100 carries information at multiple phase angles within eachsinusoidal period, thereby allowing 2, 4, or more symbols to betransmitted during each period. The amount of information conveyedduring each period is a function of the carrier frequency and modulationpoints within the period (not the spectrum used). In this sense the datatransmission rate may be characterized in terms of bits per sine waveperiod rather than in terms of, for example, bits per Hertz.

In one embodiment a digital representation of the modulated sine wave100 is directly generated as a sequence of voltage points using asoftware-defined radio (SDR). This sequence of voltage points may thenbe provided to a digital to analog converter for generation of acorresponding analog version of the modulated sine wave 100. It has beenfound that in order to minimize the creation of sidebands the modulatedsine wave should not exceed the trace or boundaries of an unmodulatedsine wave of the same frequency. That is, the modulated sine wave shouldideally be of the same frequency and phase as an unmodulated sine waveand have an amplitude magnitude less than that of the unmodulated sinewave at all phase angles. Stated differently, a modulated sine wave maybe created by generating an unmodulated sine wave having its outputpower reduced at or near the phase angles of 45°, 135°, 225° and 315° soas to create a set of modulation perturbations during some or all sinewave periods. The reduction in power associated with generating themodulation perturbations should ideally not exceed a point where a phaseshift would be triggered. It has further been found that the creation ofsidebands is most favorably minimized when (i) an energy correspondingto the cumulative power reduction occurring over the modulationperturbation at 45° matches an energy corresponding to the cumulativepower reduction occurring over the modulation perturbation at 225°, and(ii) an energy corresponding to the cumulative power reduction occurringover the modulation perturbation at 135° matches an energy correspondingto the cumulative power reduction occurring over the modulationperturbation at 315°. As discussed below, single or multiple layers ofpower reductions can be used to increase throughput.

With reference now to FIG. 5, a table 112 showing the location of thenotches on the modulated sine wave 100 shown in FIG. 4 is presented.From a review of the table 112 it should be noted that a notch may bemulti valued. In particular, the power of the notch 104 present at 45°is 30% less than the wave power and has a value of 1. The power of thenotch 106 present at 135° is 15% less than the wave power and has avalue of 0. The power of the notch 108 present at 225° is 15% less thanthe wave power and has a value of 0. Lastly, the power of the notch 110present at 315° degrees is 30% less than of the wave power and has avalue of 1. While the number of notches may vary, in the embodiment ofFIG. 4 the number of notches used is four. As may be appreciated fromFIGS. 4 and 5, the modulated sine wave 100 is capable of providing atleast four data bits per wave. These four notches may represent fourdata bits such that, for example, a wave frequency of 400 MHz providesfor a 1.6 gigabit data stream.

FIG. 6 illustrates another form of a modulation perturbation 120 whichmay be utilized to encode data proximate the 45° phase angle. As shown,the modulation perturbation 120 defines a plurality of transitions inthe form of steps 126, 128, 130, and 132. In the example of FIG. 6 theseplurality of transitions 126, 128, 130, and 132 present a value of 1111that may be transmitted as part of the modulation perturbation 120.

Referring now to FIG. 7, another exemplary modulation perturbation 140which may be utilized to, for example, encode data proximate a phaseangle of 135° is shown. As shown, the modulation perturbation 140defines a plurality of transitions in the form of steps 146, 148, 150,and 152 to present a value of 1010 that is conveyed when the modulationperturbation 140 is transmitted.

FIG. 8 depicts an exemplary modulation perturbation 160 which may beutilized to, for example, encode data proximate a phase angle of 225°.As shown, the modulation perturbation 160 defines a plurality oftransitions in the form of steps 166, 168, 170, and 172. In oneembodiment these transitions 166, 168, 170, and 172 are representativeof a value of 1111 that is conveyed when the modulation perturbation 160is transmitted.

Turning now to FIG. 9, an illustration is provided of an exemplarymodulation perturbation 180 which may be utilized to, for example,encode data proximate a phase angle of 315°. The modulation perturbation180 defines a plurality of transitions in the form of steps 186, 188,190, and 192. In one embodiment these transitions 186, 188, 190, and 192are representative of a value of 1011.

As can be appreciated, a relatively higher number of data bits per sinewave period may be transmitted by the system 10 by using modulationperturbations having a plurality of transitions to modulate theamplitude of a sine wave. As discussed above, each of the modulationperturbations 120, 140, 160 and 180 may represent multiple bits of datarather than a single bit of data.

In the embodiments of FIGS. 6-9, it has been found that the creation ofsidebands is most favorably minimized when (i) an energy correspondingto the cumulative power reduction occurring over the multi-bitmodulation perturbation at 45° matches an energy corresponding to thecumulative power reduction occurring over the multi-bit modulationperturbation at 225°, and (ii) an energy corresponding to the cumulativepower reduction occurring over the multi-bit modulation perturbation at135° matches an energy corresponding to the cumulative power reductionoccurring over the multi-bit modulation perturbation at 315°. In thissense power reduction refers to the extent to which the power of anunmodulated sine wave is reduced at a given phase angle in order todefine the modulation perturbation at that phase angle. The cumulativepower reduction over a modulation perturbation corresponds to theintegral over time of the power reductions at the phase angles subtendedby the modulation perturbation (e.g., 44.5° to 45.5° for a modulationperturbation at 45°).

With particular reference now to FIG. 10, an example of a modulatedsinusoidal waveform 200 is shown in which the letter H is shown encodedinto the modulated sinusoidal waveform 200 for transmission by thesystem 10. By way of example only, the letter H may be transmitted inthe following manner. The letter H in ASCII (American Standard Code forInformation Interchange) code is defined as 01001000. As can beappreciated, in ASCII code there are 8 bits per letter, so it wouldrequire two sine waves periods (4 bits per sine wave period) per letterto transmit the letter H when single-bit modulation perturbations (FIGS.4 and 5) are utilized. The modulated sinusoidal waveform 200 consists ofa sinusoidal wave 202 having a first wave of period 204. The sinusoidalwave 202 is disturbed or notched at a first angle 206 of 45° in whichthe power of the sinusoidal wave 202 is reduced by 15%. In theembodiment of FIG. 10 this degree of power reduction relative to anunmodulated sine wave represents a zero or 0 bit. The sinusoidal wave202 is also disturbed or notched at a second angle 208 of 135° in whichthe power of the sinusoidal wave 202 is reduced by 30%. In theembodiment of FIG. 10 this degree of power reduction relative to anunmodulated sine wave represents a one or 1 bit. Next, during the firstperiod 204, the sinusoidal wave 202 is disturbed or notched at a thirdangle 210 of 225°, in which the power of the wave 202 is reduced by 15%in order to represent a 0 bit. The sinusoidal wave 202 is disturbed ornotched at a fourth angle 212 of 315° in which the power of the wave 202is reduced by 15% to represent a 0 bit. The power reductions of 15% and30% are merely exemplary and in other embodiments other combinations ofpower reductions may be utilized.

As shown in FIG. 10, the sinusoidal wave 202 has a second wave period214. In the second wave period 214 the sinusoidal wave 202 is disturbedor notched at a first angle 216 of 45° in which the power of the wave202 is reduced by 30%. Again, this modulation perturbation isrepresentative of a 1 bit. The sinusoidal wave 202 is then disturbed ornotched at a second angle 218 of 135° in which the power of the wave 202is reduced by 15% to correspond to a 0 bit. Next, during the secondperiod 214, the sinusoidal wave 202 is disturbed or notched at a thirdangle 220 of 225° in which a modulation perturbation is created byreducing the power of the wave 202 by 15% relative to an unmodulatedsinusoid. This is symbolic of a 0 bit being transmitted. Lastly, thesinusoidal wave 202 is disturbed or notched at a fourth angle 222 of315° in which the power of the wave 202 is reduced by 15% relative to anunmodulated sinusoid. In the embodiment of FIG. 10, two waves or periods204 and 214 (4 bits per wave or period) were used to transmit the letterH in ASCII code.

FIG. 11 illustrates an example of a modulated sinusoidal waveform 250 inwhich the word HELLO is shown encoded into the modulated sinusoidalwaveform 250 for transmission by the system 10. The word HELLO may betransmitted in the following manner By use of ASCII code, the letter His defined as 01001000, the letter E is defined as 01100101, the letterL is defined as 01101100, and the letter O is defined as 01101111. Inorder to transmit the word HELLO, only ten waves or sine wave periodswould be required when using single-bit modulation perturbations (FIGS.4 and 5). In embodiments utilizing multi-bit modulation perturbations(FIGS. 6-9), even fewer sine wave periods would be required to transmitthe word HELLO.

As may be appreciated, there are 8 bits per letter in ASCII code and soit would require two sine wave periods (4 bits per period) per letter totransmit the word HELLO by use of a sine wave that is modulated usingsingle-bit modulation perturbations. The bit pattern for the word HELLOthat appears in FIG. 11 should be transmitted by the system 10 ispresented as follows: 0100100001100101011011000110110001101111. As canbe appreciated, the modulated sine wave 250 consists of ten periods 252,254, 256, 258, 260, 262, 264, 266, 268, and 270. In the first period 252and the second period 254 the letter H is presented. The periods 252 and254 correspond to the periods 204 and 214 shown in FIG. 10. The periods256 and 258 are representative of the letter E. The periods 260 and 262represent the first letter L and the periods 264 and 266 represent thesecond letter L. Finally, the periods 268 and 270 represent the letterO. By way of example only, in the periods 268 and 270, the bit pattern01101111 is being transmitted. In particular, the period 268 has a firstnotch 272 at an angle of 45° in which the power of the wave 250 isreduced by 15%, a second notch 274 at an angle of 135° in which thepower of the wave 250 is reduced by 30%, a third notch 276 at an angleof 225° in which the power of the wave 250 is reduced by 30%, and afourth notch 278 at an angle of 315° in which the power of the wave 250is reduced by 15%. The period 270 has a first notch 280 at an angle of45° in which the power of the wave 250 is reduced by 30%, a second notch282 at an angle of 135° in which the power of the wave 250 is reduced by30%, a third notch 284 at an angle of 225° in which the power of thewave 250 is reduced by 30%, and a fourth notch 286 at an angle of 315°in which the power of the wave 250 is reduced by 30%. The wave 250 mayhave another period 288 in which a parity bit or an error detection codeis incorporated into the wave 250.

Although in the embodiments of FIGS. 10 and 11 data is encoded bymodulation perturbations in the form of notches at phase angles of 45°,135°, 225° and 315° during each sine wave period, other notchpermutations are possible provided that the energy associated withnotches in opposite IQ quadrants remains balanced. For example, duringcertain sine wave periods no notches may be present. During otherperiods notches may be presently only at, for example, phase angles of45° and 225°. Alternatively notches may be present only at phase anglesof 135° and 315°. Moreover, the power reductions corresponding tonotches representing a data value of “0” and a data value of “1” neednot be only 15% and 30%, respectively. Other combinations of powerreductions may be utilized to create notches representing data of “0”and “1” values in other embodiments.

It has been found that the modulated sine waves described herein may bedigitally generated in such a way so as to substantially avoid thecreation of harmonics and sidebands. This is believed to be asignificant departure from the prior art, in which conventionalmodulation of sinusoids induces the creation of harmonics and sidebands.Such conventional techniques then typically require that either thesinusoidal carrier or the sidebands be suppressed or otherwise filtered.

In contrast the bandwidth occupied by a modulated sine wave generatedconsistent with the energy balancing principles described herein canbecome vanishingly small and be dependent only upon the accuracy of theequipment used (e.g., on the phase noise and jitter of such equipment).That is, it has been found that the disclosed periodic modulationtechniques may be implemented such that the bandwidth of the resultingmodulated sine wave is essentially independent of the appliedenergy-balanced modulation. Stated differently, under ideal conditionsthe energy-balanced modulation does not appear to contribute to thebandwidth of the resulting-modulated sine wave. As a consequence,extremely efficient use of spectrum may be achieved since adjacentmodulated sinusoids may be spaced extremely closely (e.g., at spacingsof 10 Hz to 15 Hz, or even closer).

The use of this extremely narrow band signal also allows an extremelyhigh sensitivity, as there is almost no noise in this narrow band andonly 4 (out of 360) phase angle positions per period are relevant fordemodulation. The improvement in sensitivity is therefore caused both bya very narrow channel and a limited use of the signal in the timedomain. In general, the sensitivity of the receiver has been found to becommensurate with the sampling rate of the A/D converter.

As noted above, it has been found that in order to substantially avoidthe creation of side bands and harmonics when implementing sub-periodicsine wave modulation, the integral of the reduction of the output powerat the modulation points which are opposite of each other in an I/Qdiagram are required to be substantially equal.

FIGS. 12A and 12B illustrate the manner in which this energy-balancingprinciple is applied to the case in which each modulation perturbationis representative of a single data bit (4 data bits per sine wave periodare encoded). This is achieved by reducing the time (or angle) of theoutput power of a 30% reduction (representative of a first data value,e.g., a “1”) to about half of the time (or angle) of a 15% powerreduction (representative of a second data value, e.g., a “0”). Theedges where the pure oscillator sine wave enters the power reducedmodulation point and where it renters it after the modulation pointshould ideally be smoothed out.

In the embodiment of FIGS. 12A and 12B, the data values of 0, 0, 0 and 1are encoded by modulation perturbations created at the phase angles 45°,135°, 225° and 315°, respectively. In this embodiment, the integral inthe reduction of the output power relative to an unmodulated sinusoidarising from the modulation perturbation at 45° is substantially equalto the integral of the reduction of the output power relative to anunmodulated sinusoid arising from the modulation perturbation at 225°.Similarly, the integral in the reduction of the output power relative toan unmodulated sinusoid arising from the modulation perturbation at 135°is substantially equal to the integral of the reduction of the outputpower relative to an unmodulated sinusoid arising from the modulationperturbation at 315°.

In FIG. 12A, a first modulation perturbation (1) is at a phase angle Θ₁of 45° and subtends an angle ΔΘ₁ of approximately 1° between 44.5° and45.5° (not shown to scale). A second modulation perturbation (2) is at aphase angle Θ₂ of 315° and subtends an angle ΔΘ₂ of approximately 0.5°between 314.5° to 315.5°. A third modulation perturbation (3) is at aphase angle Θ₃ of 225° and subtends an angle ΔΘ₃ of approximately 1°between 224.5° and 225.5°. A fourth modulation perturbation (4) is at aphase angle Θ₄ of 135° and subtends an angle ΔΘ₄ of approximately 1°between 134.5° and 135.5°. In order to achieve energy balancing of theenergies associated with modulation perturbations at 45° and at 225°,and energy balancing of the energies associated with modulationperturbations at 135° and at 315°, values of the modulated sinusoiddefining transitions into and out of the modulation perturbations may bemodified. Alternatively or in addition, the angles subtended by themodulation perturbations may be modified in order to achieve such energybalancing.

In certain embodiments data may not be encoded at each of the four phaseangles identified in FIG. 12; that is, at 45°, 135°, 225° and 315°.However, to preserve energy balance an energy-balancing power reductionis made to occur at each phase angle in the IQ diagram opposite a phaseangle at which a modulation perturbation is used to encode data. Forexample, if a modulation perturbation is used to encode one or more datavalues proximate a phase angle of 45°, then an energy reductionequivalent to the energy associated with the modulation perturbation at45° is made to occur by disturbing the sinusoid with an energy-balancingperturbation proximate a phase angle of 225°. In one embodiment thisenergy balancing is achieved by simply replicating the modulationperturbation used at 45° with an identical energy-balancing perturbationat 225°.

Attention is now directed to FIG. 13, which is an IQ diagram for anenergy-balanced modulated sine wave in which each modulationperturbation is representative of five data bits (20 data bits per sinewave period). Although in the embodiment of FIG. 13 each modulationperturbation represents five bits of an input data stream, in otherembodiments each modulation perturbation may include a greater or fewernumber of transitions in order to represent a greater or fewer number ofdata bits, respectively. In the embodiment of FIG. 13, the minimum powerlevel within the notch created by each modulation perturbation is 30%less than the power of an unmodulated sinusoid which would otherwiseexist at the same phase angle in the absence of the modulationperturbation. Rather than encoding data bits by varying such a reductionin power level between two predefined values (e.g., between 15% and30%), in the embodiment of FIG. 13 data is encoded based upon thesteepness and/or number of the transitions defined by each modulationperturbation.

In order to preserve energy balance in the modulated sine wave of FIG.13, the modulation perturbations which are 180 degrees apart in the IQdiagram are constructed to define step transitions on opposite sides ofthe notches respectively defined by such modulation perturbations. Forexample, at phase angle “1” in FIG. 13 a steep power reduction of 30%(other percentages are possible) is defined by an initial portion of thenotch (left side of the notch) and step transitions encoding input databits are defined on a return path to the original 100% power point(right side of the notch). In order to maintain energy balance, thisprocess is reversed at phase angle “3”. At this phase angle the steptransitions encoding input data bits are performed first (left side ofthe notch defined by the modulation perturbation at phase angle “3”) andthe steep and substantially linear back to 100% power is performedsecond (right side of the notch). The same process is applied withrespect to the paired modulation perturbations at the phase angles “2”and “4”, respectively.

Each modulation perturbation illustrated in FIG. 13 subtends a phaseangle of approximately 1°, although in other embodiments and/or toachieve energy balancing each modulation perturbation may subtend phaseangles larger or smaller than 1°. In FIG. 13, a first modulationperturbation (1) is at a phase angle Θ₁ of 45° and subtends an angle ΔΘ₁of approximately 1° between 44.5° and 45.5° (not shown to scale). Asecond modulation perturbation (2) is at a phase angle Θ₂ of 315° andsubtends an angle ΔΘ₂ of approximately 1° between 314.5° to 315.5°. Athird modulation perturbation (3) is at a phase angle Θ₃ of 225° andsubtends an angle ΔΘ₃ of approximately 1° between 224.5° and 225.5°. Afourth modulation perturbation (4) is at a phase angle Θ₄ of 135° andsubtends an angle ΔΘ₄ of approximately 1° between 134.5° and 135.5°. °.In order to achieve energy balancing of the energies associated withmodulation perturbations at 45° and at 225°, and energy balancing of theenergies associated with modulation perturbations at 135° and at 315°,values of the modulated sinusoid defining transitions into and out ofthe modulation perturbations may be modified. Alternatively or inaddition, the angles subtended by the modulation perturbations may bemodified in order to achieve such energy balancing.

In the embodiment of FIG. 13, the integral in the reduction of theoutput power of the modulated sinusoid across the phase angle of 1°subtended by the first modulation perturbation (1) is substantiallyequal to the integral of the reduction of the output power of themodulated sinusoid across the phase angle of 1° subtended by the thirdmodulation perturbation (3). Similarly, the integral in the reduction ofthe output power of the modulated sinusoid across the phase angle of 1°subtended by the second modulation perturbation (2) is substantiallyequal to the integral of the reduction of the output power of themodulated sinusoid across the phase angle of 1° subtended by the fourthmodulation perturbation (4).

In one embodiment the integral in the reduction of the output power ofthe modulated sinusoid over each 0.1° subtended by the first modulationperturbation (1) is substantially equal to the integral of the reductionof the output power of the modulated sinusoid over each corresponding0.1° subtended by the third modulation perturbation (3). Similarly, inthis embodiment the integral in the reduction of the output power of themodulated sinusoid over each 0.1° subtended by the second modulationperturbation (2) is substantially equal to the integral of the reductionof the output power of the modulated sinusoid over each corresponding0.1° subtended by the fourth modulation perturbation (4).

Although FIG. 13 depicts modulation perturbations having a particularnumber of step transitions, in other embodiments modulationperturbations having differing numbers or shapes of such transitions orother gradations may be utilized provided that energy balance ismaintained among such perturbations in accordance with the teachingsherein. For example, in the embodiment of FIG. 13 the modulationperturbations in diagonally opposite quadrants of the IQ diagram eachinclude a matching number of transitions but such transitions arearranged on opposite sides of the notches defined by the perturbations.In other embodiments the modulation perturbations in diagonally oppositequadrants of the IQ diagram may include differing numbers oftransitions. Moreover, although in FIG. 13 the modulation perturbationsinclude transitions on either the upslope or downslope of theirrespective notches, in other embodiments transitions or other gradationsmay be included on both the upslope and the downslope of one or more ofthe notches.

As may be appreciated by reference to FIGS. 4 and 10-13, only arelatively small portion of each modulated sine wave is used to actuallyencode information. Specifically, only the portions of each modulatedsine wave defining modulation perturbations are involved in representingor otherwise encoding data. The remainder of each modulated sine wavemay therefore considered to be redundant and of lesser importance, sincethis redundant sine wave portion does not itself function to encode orrepresent data.

It has been recognized that the redundant nature of the portions of eachmodulated sine wave outside of the modulation perturbations can beexploited to increase spectral efficiency. For example, since only asmall part of each modulated sine wave is used to represent data, it hasbeen found that multiple modulated sine waves may occupy the samefrequency if they are appropriately separated in phase so that theirrespective modulation perturbations do not overlap.

Attention is now directed to FIG. 14, which is a block diagram of anenergy-balancing transmitter 1400 in accordance with the disclosure. Asshown, the transmitter 1400 includes a data optimization and forwarderror correction (FEC) module 1410, an energy balancing coder 1420, asub-periodic time domain modulator 1430 and a digital to analogconverter 1440. The data optimization and FEC module 1410 may include,for example, a BCH encoding unit 1416 to which the input data isprovided and an AES 128 module 1414. The BCH block 1416 facilitatesdetection in the receiver by pre-processing the input data to make thenumber of “1” values within the data substantially equal to the numberof “0” values within the data. The AES 128 unit 1414 also aids indetection in the receiver by processing the BCH-encoded input data tolimit the run length of strings of the same data value.

Consistent with the AES 128 protocol, 16 bits of BCH-encoded data fromthe BCH encoding unit 1416 are provided to the AES 128 module 1414 andprocessed over multiple rounds in accordance with an encryption key. TheAES 128 module 1414 is not intended to encrypt the data, but can be usedfor encryption. The resulting cypher output produced by the AES 128module 1414 is then provided to the energy balancing coder 1420.

During operation of the transmitter 1400, the input data buffer istransferred to the AES128 module 1414 and processed in accordance with aknown key (e.g., 0x47). Again, in one embodiment the primary task of theAES 128 module 1414 is to achieve a uniform distribution of the bits toprevent a series of 0 bits from following each other. At this point thedata produced by the AES 128 module 1414 is then transferred to theenergy-balancing coder 1420.

As discussed herein, the energy balancing coder 1420 generates, computesor otherwise defines modulation perturbations at selected sine wavephase angles such that substantially equal energy is associated withmodulation perturbations in opposite quadrants of an IQ diagramrepresentative of a modulated sine wave produced by the transmitter1400. Again, it has been found that such energy balancing essentiallyinhibits the formation in connection with the sine wave modulationeffected by the transmitter 1400. As a consequence, modulated sine wavescan be spaced much more closely than is possible using conventionalmodulation schemes, thereby enabling dramatically higher spectralefficiency to be achieved.

The energy balancing coder 1420 includes a control matrix 1424 whichcontains the same number of ones (row and column weight) in each row andeach column; that is, the control matrix 1424 is a regular matrix. Therow weight does not have to correspond to the size of the column weight.

In one embodiment the energy balancing coder 1420 is configured toencode the sequence provided by the data optimization and FEC module1410 by creating modulation perturbations at the phase angles 45°, 135°,225° and 315°, respectively. In this embodiment, the integral in thereduction of the output power relative to an unmodulated sinusoidarising from the modulation perturbation at 45° is substantially equalto the integral of the reduction of the output power relative to anunmodulated sinusoid arising from the modulation perturbation at 225°.Similarly, the integral in the reduction of the output power relative toan unmodulated sinusoid arising from the modulation perturbation at 135°is substantially equal to the integral of the reduction of the outputpower relative to an unmodulated sinusoid arising from the modulationperturbation at 315°.

Attention is now directed to FIG. 15, which is a block diagram of areceiver 1500 configured to demodulate and decode a modulated sine wavegenerated by, for example, the transmitter 1400. As shown, the receiver1500 includes an analog to digital converter (ADC) 1510 operative tocreate a multi-bit representation the received modulated sine wavesignal. The digital samples of the received signal are provided to aninput buffer 1518 of a zero-crossing detector 1520. Upon detecting azero crossing within the samples stored within the input buffer 1518,the zero-crossing detector 1520 generates a zero cross detection signal1524. In response to the zero cross detection signal 1524, a sine wavesubtraction circuit 1530 begins a sine wave subtraction process pursuantto which a digital representation of an unmodulated sine wave aligned inphase with the received modulated sine wave signal is subtracted fromthe digital samples of the modulated sine wave signal. The sequence ofdigital values resulting from this subtraction process are then storedwithin a ring buffer 1540 incorporating a preamble detector 1542configured to detect a preamble inserted into the input data streamprovided to the transmitter 1400. Once the preamble has been detected,the received data stream is provided to a decoder 1550 configured toperform the inverse of the operations performed by the AES module 1414and BCH encoding module 1416. A periodic time domain demodulator 1560then identifies the modulation perturbations present within the datastream produced by the decoder 1550 and generates a recovered datastream corresponding to an estimate of the input data provided to thetransmitter 1400.

Attention is now directed to FIG. 16, which is a functional blockdiagram of an embodiment of an energy-balancing transmitter 1600suitable for implementation using a field programmable gate array(FPGA). As shown, the transmitter 1600 includes an input buffer 1604 forstoring digital input data 1608, a data optimization unit in the form ofan AES encryption module 1610, an LDPC coder 1620 and a serial-to-framedata converter 1630.

A sub-periodic time domain modulator 1640 encodes data frames providedby the data converter 1630 by perturbing sinusoidal waveforms in anenergy-balanced fashion. As shown, the sub-periodic time domainmodulator 1640 includes a pattern matching unit 1644, a sine wave lookuptable 1648, a time generator 1652 and a wave buffer 1656. The perturbedand energy-balanced waveforms produced by the modulator 1640 are storedin the wave buffer 1656 and optionally pre-distorted or otherwisefiltered by a filter 1660 prior to being converted to analog signals bya digital-to-analog converter 1664. The resulting encoded analog signalsand transmitted using for example, a transmission line or antenna.

FIG. 17 is a flowchart 1700 representative of an exemplary sequence ofencoding and other operations performed by the energy balancingtransmitter 1600 in accordance with an embodiment. Once input data hasbeen stored within the input buffer 1604 (stage 1710), it is provided tothe AES encryption module 1610. In one embodiment the AES encryptionmodule 1610 aids in detection of the data at a receiver by processingthe input data to limit the run length of strings of the same logicalvalue (stage 1712). The resulting output produced by the AES encryptionmodule 1610 is provided to the LDPC coder 1620, which performslow-density parity-check (LDPC) error correcting coding operations(stage 1716). The serial data stream produced by the LDPC coder 1620 isthen converted into a sequence of 4-bit data frames by theserial-to-frame data converter 1630 (stage 1720).

The 4-bit data frames produced by the converter 1630 are provided to thepattern matching unit 1644. During operation of the energy balancingtransmitter 1600, the pattern matching unit 1644 identifies one of 16notched sine wave stored within sine wave lookup table 1648corresponding to the 4-bit data frame currently registered within thepattern matching unit (stage 1724). In one embodiment the sine wavelookup table 1648 stores data values (e.g., 3600 data values)corresponding to a single period of each of 16 notched sine waves havingnotch patterns corresponding to each of the 16 possible values of the4-bit data frames provided to the pattern matching unit 1644. The datavalues defining each successive notched sine wave are then read from thesine wave lookup table 1648 (stage 1728) and stored within the wavebuffer 1656 (stage 1732).

In one embodiment each of the 16 notched sine waves stored within thesine wave lookup table 1648 defines modulation perturbations at selectedsine wave phase angles such that substantially equal energy isassociated with modulation perturbations in opposite quadrants of an IQdiagram. Again, it has been found that such energy balancing essentiallyinhibits the formation of sidebands in connection with the sine wavemodulation effected by the transmitter 1600. As a consequence, modulatedsine waves can be spaced much more closely than is possible usingconventional modulation schemes, thereby enabling dramatically higherspectral efficiency to be achieved.

In one embodiment the modulation perturbations defined by each of thenotched sine waves stored in the sine wave lookup table 1648 are at thephase angles 45°, 135°, 225° and 315°, respectively. In this embodiment,the integral in the reduction of the output power relative to anunmodulated sinusoid arising from the modulation perturbation at 45° issubstantially equal to the integral of the reduction of the output powerrelative to an unmodulated sinusoid arising from the modulationperturbation at 225°. Similarly, the integral in the reduction of theoutput power relative to an unmodulated sinusoid arising from themodulation perturbation at 135° is substantially equal to the integralof the reduction of the output power relative to an unmodulated sinusoidarising from the modulation perturbation at 315°. In one embodiment amodulation perturbation corresponding to a logical 0 subtends an angleof approximately 1 degree about the selected phase angle and defines anamplitude reduction of approximately 15% relative to an unmodulatedsinusoid. In this embodiment a modulation perturbation corresponding toa logical 1 subtends an angle of approximately 0.5 degrees about theselected phase angle and defines an amplitude reduction of approximately30% relative to an unmodulated sinusoid.

The time generator 1652 provides a clocking signal to the wave buffer1656 so that a relatively constant data rate is maintained into thefilter 1660. Since the data rate of the input data provided to the inputbuffer 1604 may be somewhat bursty or otherwise irregular, the timegenerator 1652 functions to essentially remove the resulting jitter fromthe data stream produced by the sine wave lookup table 1648 before it isprovided to the filter 1660.

In one embodiment the transmitter 1600 includes a frequencymonitoring/flow control module 1670 operative to control the data rateinto the sub-periodic time domain modulator 1640. Specifically, the flowcontrol module 1670 monitors the data rate into the pattern matchingunit 1644 and into the wave buffer 1656. When the data rate into thepattern matching unit 1644 begins to exceed the data rate into the wavebuffer 1656, the flow control module 1670 sends 4-bit frames from thepattern matching unit 1644 or serial-to-frame data converter 1630 backto the input buffer 1604 until these data rates are equalized (stage1736).

The digital representations of the notched and energy-balanced sinewaves stored within the wave buffer 1656 are optionally pre-distorted orotherwise filtered by the filter 1660 in order to compensate forquantization errors introduced by the digital-to-analog converter 1664(stage 1740). In one embodiment this filtering may comprise introducinga pre-distortion having a power spectra in the frequency domainequivalent to the power spectra expected to be induced by suchquantization errors, phase-shifted by 180 degrees. The filtered digitalsignal produced by the filter 1660 is then converted to an encodedanalog signal by the DAC 1664 and transmitted via either a wired orwireless communication medium (stage 1744).

Attention is now directed to FIG. 18, which is a functional blockdiagram of an another embodiment of an energy-balancing transmitter 1800suitable for implementation in, for example, an FPGA. Except asdescribed below, the structure and function of the transmitter 1800 issubstantially identical to the structure and function of theenergy-balancing transmitter 1600 of FIG. 16. Accordingly, likereference numerals are used in FIGS. 16 and 18 to identify substantiallyidentical transmitter components. As may be appreciated with respect toFIGS. 16 and 18, the structure of the transmitter 1800 differs from thatof the transmitter 1600 in that the time domain modulator 1640additionally includes a notched sine wave generator 1810 and a modeswitch 1820. These additional elements are intended to enable thetransmitter 1800 to operate at relatively higher data rates and arediscussed below.

Referring now to FIG. 19, a flowchart 1900 is provided which isrepresentative of an exemplary sequence of encoding and other operationsperformed by the energy balancing transmitter 1800 in accordance with anembodiment. Given the similarity in the structure and function of thetransmitter 1800 and the transmitter 1600 of FIG. 16, like referencenumerals are used in the flowcharts of FIGS. 17 and 19 to identifysubstantially identical operations.

During operation of the transmitter 1800, the sub-periodic time domainmodulator 1640′ determines whether the data rate of the 4-bit framesprovided to the pattern matching unit 1644 exceeds a predefined datarate (stage 1910). At relatively lower data rates, i.e., at data ratesless than the predefined data rate known to the modulator 1640′, thedata points defining the notched sine wave corresponding to the 4-bitframe registered in the pattern matching unit 1644 are read out from thesine wave lookup table 1648 and provided to the wave buffer 1656 via themode switch 1820 (stage 1728). In one embodiment the predefined datarate is set to the data rate at which the stored data defining thenotched sine waves may be read out from the sine table 1648. Because inone embodiment a relatively large number of points (e.g., 3600) are usedto define each notched sine wave, at higher data rates the I/Ocapabilities of certain memory implementations may be insufficient tosupport desired input data rates. Accordingly, in one embodiment thedata points defining the notched sine waves corresponding to the 4-bitframes sequentially registered in the pattern matching unit 1644 aregenerated “on the fly” by the notched sine wave generator 1810 ratherthan being read out from the sine table 1648.

In this embodiment the notched sine wave generator 1810 may beconfigured to generate a set of data points (e.g., 360 data points) foran unmodulated sine wave by simply executing a processing loop whichsolves the equation for a sine wave at a set of phase angles (e.g., ateach of 360 degrees). In this example the 10 or so data points definingthe contour of the unmodulated sine wave around each phase angle atwhich a data notch is to be created (i.e., 45°, 135°, 225° and 315°) arereplaced with an equal number of data points defining the notch pattern(e.g., 1,0,1,1) corresponding to the 4-bit data frame registered by thepattern matching unit 1644 (stage 1920). The resulting set of datapoints (e.g., 360 data points) are then provided to the wave buffer 1656by the mode switch 1820 (stage 1732). Although this approach offers lessresolution in defining the data notch patterns of each notched sine waverelative to the higher-resolution approach in which a large number ofdata points (e.g. 3600) are pre-stored within the sine table 1648 foreach notched sine wave, it enables higher input data rates to beaccommodated. The data flow control, filtering and digital-to-analogconversion processes are then performed in the manner described abovewith reference to FIGS. 16 and 17 once the data points defining eachnotched sine wave have been placed in the wave buffer 1656.

Alternatively, the notched sine wave generator 1810 may be configured togenerate a set of data points (e.g., 360 data points) by executing aprocessing loop which generates a modulated sine wave having a datanotch defining a logical “0” at each of the four phase angles ofinterest (i.e., 45°, 135°, 225° and 315°). In this example the 10 or sodata points about each phase angle of interest would be replaced only ifthe 4-bit data frame registered by the pattern matching unit 1644 calledfor a logical “1” at the phase angle of interest. For example, a 40-bitframe of [1,0,0,1] could require that the 10 data points around each of45° and 315° be replaced with sets of data points defining a logical “1”rather than a logical “0”.

It is a feature of the energy balancing techniques described herein thatmodulation perturbations may be imposed upon a sinusoidal waveform atselected phases without creating sidebands of material power (e.g., 50dB or more below the power of the sine wave at its carrier frequency).This permits modulated sine waves generated in accordance with thedisclosure to be spaced very closely without materially interfering witheach other. For example, it has been found that such modulated sinewaves may be spaced apart in frequency by less than 15 Hz. This enablesa given band of spectrum to be utilized more efficiently than ispossible using conventional modulation techniques.

In one embodiment each modulated sine wave carrier within amulti-carrier system is modulated using modulation perturbations ofsimilar type. For example, in one implementation each of the modulatedcarriers is modulated using modulation perturbations including a numberof step transitions (see FIG. 13). In other embodiments each of themodulated carriers is modulated using modulation perturbations comprisedof notches representing 1 data bit (see FIG. 10). Although in someembodiments modulated sine waves occupying adjacent frequency slots(e.g., frequencies separated by 15 Hz or less) are generated usingmodulation perturbations of different types, it has been found thatperformance is improved if modulation perturbations of the same type areused in generating adjacent modulated sine waves.

Attention is now directed to FIG. 20, which is a block diagramrepresentation of a multi-carrier energy-balancing transmitter 2000 inaccordance with an embodiment. As shown, the transmitter 2000 includesan input buffer 2010 in which input data from an external source isstored. The stored data within the input buffer 2010 is allocated amonga plurality (N) of modulated, energy-balanced sine wave carriers by acontroller 2020. Specifically, controller 2020 directs streams of inputdata to a set of N energy-balancing transmitters 2030. Each of the Ntransmitters 2030 modulates a sine wave carrier in accordance with itsstream of input data from the input buffer 2010 so as to produce amodulated, energy-balanced since wave. In one embodiment each of the Ntransmitters 2030 may be substantially identical to, for example, theenergy-balancing transmitter 1600 or the energy-balancing transmitter1800 and may be implemented as a separate cell of an FPGA.

In one embodiment the controller 2020 routes data from the input buffer2410 to a first of the transmitters 2030 ₁ until the input data rateexceeds the maximum data rate of the first transmitter 2030 ₁. At thispoint the controller may provide data to both the first transmitter 2030₁ and one or more other of the remaining N−1 transmitters 2030. Otherdata allocation strategies are possible. For example, a fixed amount ofdata from the input buffer 2410 may be provided to each of the Ntransmitters 2030 such that each transmitter 2030 operates a data rateof R/N, where R is the data rate into the input buffer 2410. Forexample, a first four data bits received by the input buffer could berouted to transmitter 2030 ₁, a second four bits received by the inputbuffer could be routed to transmitter 2030 ₂, and so on. If at somepoint the data rate into the input buffer 2010 exceeded the aggregatedata rate of the N transmitters 2030, one or more of the N transmitters2030 could send back at least some of the 4-bit data frames provided toit for buffering in the input buffer 2010.

Attention is now directed to FIG. 21, which is a functional blockdiagram of a receiver 2100 configured to receive and demodulate encodedsine waves transmitted by an energy-balancing transmitter configured inaccordance with the disclosure. For example, the receiver 2100 iscapable of receiving and demodulating encoded sine waves transmitted bythe energy-balancing transmitter 1600 or the energy-balancingtransmitter 1800. As shown, one or more energy-balanced encoded sinewaves are received by a filter 2110 of the receiver 2100 and provided toan analog-to-digital converter (ADC) 2120.

A time generator 2124 clocks or otherwise controls the output data rateof the ADC 2120. Amplitude values of each received energy-balancedencoded sine wave generated by the ADC 2120 are provided to a wavebuffer 2128. Once the receiver 2100 has achieved time synchronizationwith a received energy-balanced encoded sine wave (e.g., by detectingzero crossings of the received encoded sine wave), the ADC 2120 may begated “on” so as to only generated sample values around the data notchesof the received encoded sine wave. For example, the ADC 2120 may beturned on only for a time period equivalent to approximately one degreeof phase at phase angles of 45°, 135°, 225° and 315°. Thus, in oneembodiment sensitivity is enhanced by configuring the ADC 2120 to sampleover only a very narrow bandwidth and furthermore by only samplingduring approximately 4° of every 360° sine wave period. Whenenergy-balanced encoded sine waves of multiple carrier frequencies arebeing received, the ADC 2120 may be gated on and off so as to onlysample during the 45°, 135°, 225° and 315° phase angles of each encodedsine wave. Alternatively, a separate ADC could be used to sample eachencoded sine wave at narrow windows around the 45°, 135°, 225° and 315°phase angles of the encoded sine wave. The signal samples produced bythe ADC 2120 are provided to a wave buffer 2128.

The contents of the wave buffer 2128 are serially provided to adeserializer-to-byte unit 2134, which produces a series of logicalvalues representing the bit values encoded by the data notches of theencoded sine wave received by the receiver 2100. The logical valuesgenerated by the byte unit 2134 are then provided to an LDPC decoder2140 configured to remove the LDPC encoding applied by theenergy-balancing transmitter (e.g., the transmitter 1600 or transmitter1800) from which the encoded sine wave was transmitted. Similarly, anAES decryption unit 2146 reverses the encryption applied by acorresponding AES encryption unit in the energy-balancing transmitter.The output of the AES decryption unit 2146 may then be provided to anoutput buffer 2150. In one embodiment the receiver 2100 searches bitsequences within the output buffer 2150 for a preamble data bit string(e.g., a 0x47 string) signifying the start of a packet. In an exemplaryimplementation the encoded sine waves received by the receiver 2100carry frames of 1500 bits. Each frame begins with a predefined bitstring (e.g., 0x47) and is followed by the data being communicated. Oncethe preamble has been identified within the output buffer 2150, anestimate of the data being communicated may be provided to a local areanetwork (LAN) or the like via a network interface 2154. Alternatively,the entire contents of the output buffer 2150 may be provided to anexternal system configured to identify the preamble for each frame andrecover the data conveyed by the frame.

Attention is now directed to FIG. 22, which is a functional blockdiagram of an embodiment of an energy-balancing transmitter 2200configured to generate and transmit sinusoidal waveforms modulated withmulti-bit features at selected phase angles. In one embodiment thesemulti-bit features include notches having 4-bit stair step patterns ofthe type illustrated in, for example, FIGS. 6-9. In other embodimentsthese features may be utilized to encode 8 or more bits at each selectedphase angle. The maximum number of bits capable of being encoded at eachphase angle is believed to be limited primarily or exclusively by theresolution of the digital-to-analog and analog-to-digital converterswithin the transmitter 2200 and a corresponding receiver, respectively.

As shown, the transmitter 1600 includes an input buffer 2204 for storingdigital input data 2208, a data optimization unit in the form of an AESencryption module 2210, an LDPC coder 2220, a cyclic redundancy check(CRC) module 2224, and a 32-to-8 bit splitter 2230.

A sub-periodic time domain modulator 2240 encodes data frames providedby the bit splitter 2230 by perturbing sinusoidal waveforms in anenergy-balanced fashion. As shown, the sub-periodic time domainmodulator 2240 includes first and second pattern matching units 2244 and2245, a sine wave lookup table 2248, a time generator 2252, and a wavebuffer 2256. The modulator 2240 further includes memory for storing thesets of data points defining multi-bit data notches for each of the 45°,135°, 225° and 315° phase angles. In particular, the modulator 2240includes a 45° storage unit 2280 for storing sets of data pointsdefining multi-bit data notches for the 45° phase angle, a 135° storageunit 2282 for storing sets of data points defining multi-bit datanotches for the 135° phase angle, a 225° storage unit 2284 for storingsets of data points defining multi-bit data notches for the 225° phaseangle, and a 315° storage unit 2286 for storing sets of data pointsdefining multi-bit data notches for the 315° phase angle. Theenergy-balanced waveforms having multi-bit data notches produced by themodulator 2240 are stored in the wave buffer 2256 and optionallypre-distorted or otherwise filtered by a filter 2260 prior to beingconverted to analog signals by a digital-to-analog converter (DAC) 2264.The resulting encoded analog signals and transmitted using for example,a transmission line or antenna.

During operation of the energy-balancing transmitter 2200, input data2208 stored within the input buffer 2204 is provided to the AESencryption module 2210. In one embodiment the AES encryption module 2210aids in detection of the data at a receiver by processing the input datato limit the run length of strings of the same logical value. Theresulting output produced by the AES encryption module 2210 is providedto the LDPC coder 2220, which performs low-density parity-check (LDPC)error correcting coding operations. The serial data stream produced bythe LDPC coder 2220 is then provided to the CRC module 2224 and a bitsplitter 2230. In one embodiment in which the multi-bit data notchdefined at each of the selected phase angles of the sinusoidal waveformsincludes 8 bits (32 bits being encoded per each period of the sinusoidalwaveform), the bit splitter 2230 divides the 32 bits for each frame into4 sets of 8 bits. In this embodiment the bit splitter 2230 causes eachof the 4 sets of 8 bits for a given frame to address a different one ofthe storage units 2280, 2282, 2284 and 2286. In response, each of thestorage units 2280, 2282, 2284 and 2286 retrieves from its memory apre-computed 8-bit, stair step notch pattern corresponding to the 8-bitpattern used to address it and provides the data points defining such anotch pattern to the wave buffer 2256. In this embodiment each of the8-bit, stair step notch patterns stored by each of the each of thestorage units 2280, 2282, 2284 and 2286 is of equal area, i.e., eachstored 8-bit, stair step pattern is energy balanced with all otherstored patterns.

In another embodiment the encoded sinusoidal waveform stored in the wavebuffer 2256 encodes not only a 32-bit data frame (8 bits at each of fourphase angles) but also encodes a CRC value produced by the CRC module2224. In this embodiment the CRC value (e.g., a 4-bit value) is providedto the sine wave lookup table 2248. In this embodiment the sine wavelookup table 2248 defines a set of 16 notches sinusoidal waveforms,where the depth of each data notch at each of the four selected phaseangles is defined by one of the 4 bits of the CRC value. For example, alogical 0 in the CRC value corresponds to a data notch subtending anangle of approximately 1 degree about the selected phase angle anddefines an amplitude reduction of approximately 15% relative to anunmodulated sinusoid. A logical 1 in the CRC value corresponds to a datanotch subtending an angle of approximately 0.5 degrees about theselected phase angle and defines an amplitude reduction of approximately30% relative to an unmodulated sinusoid. So in substantially the samemanner as was described above with reference to FIG. 16, the 4-bit CRCvalue defines the span and depth of the data notches at the selectedphase angles (i.e., 45°, 135°, 225° and 315°). In addition, each of thefour 8-bit sets of data within the 32-bit data frame provided to the bitsplitter 2230 defines the stair step pattern imposed on the notches ateach of the four selected phase angles. Because for energy balancing tooccur the areas of the notches (with imposed stair step patterns) at 45°and 225° must be equal and the areas of the notches at 135° and 315°must be equal, the stair step pattern for a given 8-bit portion of thedata frame required to achieve such energy balancing may be differentdepending upon the CRC value. Accordingly, the sine table 2248 selectsthe data points defining the appropriately energy-balanced stair steppatterns from the storage units 2280, 2282, 2284 and 2286 in response tothe CRC value from the CRC module 2224 and the 32-bit data frame valueproduced by the LDPC coder 2220. In one embodiment portions of the32-bit data frame may be loaded into pattern matching units 2244 and2245.

The time generator 2252 provides a clocking signal to the wave buffer2256 so that a relatively constant data rate is maintained into thefilter 2260. Since the data rate of the input data provided to the inputbuffer 2204 may be somewhat bursty or otherwise irregular, the timegenerator 2252 functions to essentially remove the resulting jitter fromthe data stream produced by the sine wave lookup table 2248 before it isprovided to the filter 2260.

In one embodiment the transmitter 2200 includes a frequencymonitoring/flow control module 2270 operative to control the data rateinto the sub-periodic time domain modulator 2240. Specifically, the flowcontrol module 2270 monitors the data rate into the modulator 2240 andinto the wave buffer 2256. When the data rate into the modulator 2240begins to exceed the data rate into the wave buffer 2256, the flowcontrol module 2270 sends data from the pattern matching units 2244 and2245 or bit splitter 2230 back to the input buffer 2204 until these datarates are equalized.

The digital representations of the notched and energy-balanced sinewaves stored within the wave buffer 2256 are optionally pre-distorted orotherwise filtered by the filter 2260 in order to compensate forquantization errors introduced by the digital-to-analog converter 2264.In one embodiment this filtering may comprise introducing apre-distortion having a power spectra in the frequency domain equivalentto the power spectra expected to be induced by such quantization errors,phase-shifted by 180 degrees. The filtered digital signal produced bythe filter 2260 is then converted to an encoded analog signal by the DAC2264 and transmitted via either a wired or wireless communicationmedium.

Attention is now directed to FIG. 23, which is a functional blockdiagram of an another embodiment of an energy-balancing transmitter 2300configured to generate and transmit sinusoidal waveforms modulated withmulti-bit features at selected phase angles. Aspects of the structureand function of the transmitter 2300 are substantially identical tothose of the energy-balancing transmitter 2200 of FIG. 22. Accordingly,like reference numerals are used in FIGS. 22 and 23 to identifysubstantially identical transmitter components. As is discussed below,the transmitter 2300 includes an energy-balancing encoded sine wavegenerator 2310 configured to enable the transmitter 2300 to selectivelyoperate at relatively higher data rates than the transmitter 2200.

During operation of the transmitter 2300, the energy-balancing encodedsine wave generator 2310 determines whether the data rate out of theLDPC-coder 2220 exceeds a predefined data rate. At data rates below thepredefined data rate, the energy-balancing encoded sine wave generator2310 operates substantially to the sub-periodic time domain modulator2240 (FIG. 22) to produce sinusoidal waveforms encoded with multi-bitnotch features at selected phase angles. That is, the energy-balancingencoded sine wave generator 2310 relies upon pre-stored sets of datapoints defining energy-balanced data notches and recalls thesepre-computed and pre-stored data points in accordance with the inputdata being encoded. Because in one embodiment a relatively large numberof points (e.g., 3600) are used to define each encoded sine wavegenerated by the modulator 2240, at higher data rates the I/Ocapabilities of certain memory implementations may be insufficient tosupport desired input data rates. Accordingly, in the embodiment of FIG.23 the data points defining the encoded sine waves having multi-bitnotch features at selected phase angles are generated “on the fly” bythe energy-balancing encoded sine wave generator 2310 rather than beingretrieved from pre-populated data tables.

Upon determining the input data rate exceeds the predefined data rate,in one embodiment the energy-balancing encoded sine wave generator 2310performs the following sequence of operations to generate anenergy-balanced encoded sine wave having multi-bit notch features at thephase angles of 45°, 135°, 225° and 315°. First, the energy-balancingencoded sine wave generator 2310 reads in data from the LDPC coder 2220corresponding to a first multi-bit data notch at 45°. The generator 2310then determines step widths of an N-bit stair pattern to be defined inthe data notch centered at 45°. For example, relatively narrow steps inthe pattern may represent a “1” in the input data and wider steps mayrepresent a “0” in the input data. Other step-like features may be usedto represent binary values within the scope of the present disclosure.See, e.g., FIGS. 6-9. After defining the N-bit stair pattern for thedata notch at 45°, the signal energy associated with this data notch iscomputed or otherwise approximated. Again, the energy of the data notchat 45° corresponds to the cumulative difference in power between anunmodulated sine wave and the data notch over the angle subtended by thedata notch. See, e.g., FIG. 24, which illustrates an area 2410 boundedby an unmodulated sinusoid 2420 and a multi-bit data notch 2430. Thearea 2410 is related to this cumulative power difference and may bedenoted as the first master area.

Next, the energy-balancing encoded sine wave generator 2310 reads indata from the LDPC coder 2220 corresponding to a second multi-bit datanotch at 135°. The generator 2310 then determines, based upon this data,step widths of a second N-bit stair pattern to be defined in the datanotch centered at 135° and computes its area. The generator 2310 maythen either (i) adjust an area of the second notch at 135° to match thefirst master area (e.g., by adjusting bit values at the edge of thenotch width), or (ii) compute the area of the second multi-bit datanotch at 135° after defining the second N-bit stair pattern and denotethis are as the second master area.

The energy-balancing encoded sine wave generator 2310 reads in data fromthe LDPC coder 2220 corresponding to a third multi-bit data notch at225°. The generator 2310 then determines, based upon this data, stepwidths of a third N-bit stair pattern to be defined in the data notchcentered at 225° and computes its area. The generator 2310 then adjuststhe area of the third multi-bit data notch at 225° to match the firstmaster area (e.g., by adjusting bit values at the edge of the thirdmulti-bit data notch).

The energy-balancing encoded sine wave generator 2310 reads in data fromthe LDPC coder 2220 corresponding to a fourth multi-bit data notch at315°. The generator 2310 then determines, based on the data, step widthsof a fourth N-bit stair pattern to be defined in the fourth multi-bitdata notch centered at 315° and computes its area. The generator 2310then adjusts the area of the fourth multi-bit data notch at 315° tomatch the second master area (e.g., by adjusting bit values at the edgeof the fourth multi-bit data notch).

If the generator 2310 is unsuccessful in forcing the area of the secondand fourth multi-bit data notches (i.e., the multi-bit data notchescentered at 135° and 315°) and/or is unsuccessful in matching the areasof the first and third multi-bit data notches, the generator 2310 mayalter the relative positions of bits in the second and fourth multi-bitdata notches. After altering these bit positions, the generator 2310will again attempt to adjust values defining the edges of the second andfourth multi-bit data notches to cause their respective areas to match.Essentially the same bit rearrangement procedure may be followed to theextent the generator 2310 is initially unsuccessful in achieving a matchbetween the areas of first and third multi-bit data notches by, forexample, modifying the values defining edges of these notches. To theextent any data bits are reordered when defining any of the multi-bitdata notches, the changed positions may be communicated to a receiver ina separate data channel also containing the CRC information.

As discussed above, the encoded sine waves described herein may bedigitally generated in such a way so as to substantially avoid thecreation of harmonics or sidebands. Embodiments of the disclosedmodulation techniques also enable channel bandwidths containing themodulated signal energy to be 10 Hz or less. That is, the inventor hasbeen unable to discern, using conventional spectrum analyzers, anyappreciable spreading of the spectrum of the modulated signal in thefrequency domain beyond a few Hz from the carrier frequency of themodulated signal. This is believed to represent a significant advance inthe state of the art, since conventional modulation techniques typicallygenerate sidebands or otherwise utilize substantial frequency spectrum,requiring either that the sinusoidal carrier itself or the sidebandsresulting from the modulation be suppressed or otherwise filtered. Thesecharacteristics of the disclosed modulation technique permit modulatedsine waves to be spaced very closely without materially interfering witheach other, thus enabling spectrum to be utilized more efficiently thanis possible using conventional modulation techniques.

FIG. 25 is a screenshot generated by a spectrum analyzer when providedwith an encoded sinusoid modulated with data notches at 45°, 135°, 225°and 315°. Each data notch encodes 1 bit of data by being reduced inpower by 15% (for a value of 1) or 30% (for a value of 0) relative to anunmodulated sinusoid, thereby resulting in 4 bits of data being encodedduring each sine wave period. As shown, the encoded sinusoid is of afrequency of 451.75 kHz and has a measured power of −16.17 dBm, which ismore than 60 dB above an upper level 2510 of the noise floor. As may beappreciated from FIG. 25, the encoded sinusoid occupies an extremelynarrow frequency spectrum, represented by the dashed box 2520. Indeed,it is believed that the channel bandwidth occupied by the encodedsinusoid is 10 Hz or less, and that any indication to the contrary inFIG. 25 results from limitations in the capabilities of the subjectspectrum analyzer.

As may be appreciated from FIG. 25, the inventor has found that when anencoded analog waveform of a frequency f and a power P is generated froma digital representation of a sinusoid encoded at selected phase anglesusing the energy-balanced modulation techniques described herein, anysignal of frequency f′ resulting from the encoding is of a power P′ atleast 50 dB less than power P, where f′ is offset from f by more than 25Hz. Again, it is believed that this is a conservative characterizationof the benefits of the disclosed encoding scheme and is limited by thecapabilities and instant measurement settings of the subject spectrumanalyzer.

Turning now to FIGS. 26A-26C, various alternate data encoding schemes inaccordance with the disclosure are illustrated. In one embodiment asinusoid may be encoded at a pair of selected phase angles separated by180° in order to represent a single bit of data. For example, in theembodiment of FIGS. 26A-26B, encoded sinusoid 2602 may represent a valueof 0 and encoded sinusoid 2604 may represent a value of 1. As shown,encoded sinusoid 2602 includes a first data notch 2612 and a second datanotch 2614. The first data notch is centered at 135° and subtends anangle of approximately 1° and the second data notch 2614 is centered at315° and also subtends an angle of approximately 1°. In the embodimentof FIGS. 26A-26B, the areas of the first and second data notches 2612and 2614 are substantially identical and the data notches 2612 and 2614are energy balanced.

Similarly, encoded sinusoid 2604 includes a first data notch 2622 and asecond data notch 2624. The first data notch is centered at 45° andsubtends an angle of approximately 1° and the second data notch 2624 iscentered at 225° and also subtends an angle of approximately 1°. In theembodiment of FIGS. 26A-26B, the areas of the first and second datanotches 2622 and 2624 are substantially identical and the data notches2622 and 2624 are energy balanced.

FIG. 26C illustrates another manner in which sinusoids encoded atselected phase angles may be used to represent binary data. As shown,FIG. 26C depicts two periods of encoded sinusoid 2640; namely, a firstperiod T₁ and a second period T₂. In the embodiment of FIG. 26 the firstperiod T₁ of the sinusoid 264θ represents a data value of 1 and thesecond period T₂. represents a data value of 0. That is, in theembodiment of FIG. 26C the presence of the data notches 2652, 2654, 2656and 2658 at the phase angles of 45°, 135°, 225° and 315° during thefirst period T₁ represents a data value of 1, and the absence of datanotches at these phase angles represents a data value of 0. In theembodiment an energy associated with the data notch 2652 is the same asan energy associated with the data notch 2656, and an energy associatedwith the data notch 2654 is the same as an energy associated with thedata notch 2658.

FIGS. 27A and 27B illustrate sinusoids encoded in an energy-balancedmanner using data notches of alternative shapes. As shown, FIG. 27Adepicts a first encoded sinusoid 2710 having somewhat U-shaped datanotches 2712, 2714, 2716 and 2718 at the phase angles of 45°, 135°, 225°and 315°. FIG. 27B depicts a second encoded sinusoid 2740 havingsomewhat V-shaped data notches 2742, 2744, 2746 and 2748 at the phaseangles of 45°, 135°, 225° and 315°. Provided that the data notchesseparated by 180° within a given sinusoidal period are energy balanced,it has been found that the data notch shapes illustrated in FIGS. 27Aand 27B and other alternative shapes enable the encoding of informationat selected phase angles of a sinusoid without creating measurableenergy at frequencies offset from the frequency of the sinusoid by aslittle as 5 Hz.

Attention is now directed to FIG. 28, which illustrate ellipticalwaveforms encoded in an energy-balanced manner in accordance with thedisclosure. In the embodiment of FIG. 28, each elliptical waveform is ofperiod T and crosses zero at one of sixteen potential zero-crossingphases. In one embodiment a set of sixteen waveforms having differentzero crossing phases and identical periods T are employed as modulationsymbols. In particular, each symbol waveform may uniquely represent a4-bit data word corresponding to the zero-crossing phase of thewaveform. For example, a first elliptical waveform 2810 of the sixteenelliptical waveforms having a zero-crossing phase of 173° couldrepresent the data word [1001]. A second elliptical waveform 2820 havinga zero-crossing phase of 180° could, for example, represent the dataword [0000], and a third elliptical waveform 2830 having a zero-crossingphase of 187° could represent the data word [0111].

In order to minimize or eliminate the creation of sidebands or othersignal energy outside of a very narrow channel bandwidth (i.e., afrequency band of 10 Hz or less centered at the carrier frequency f,where f=1/T), it has been found that each elliptical waveform should beenergy balanced. That is, an energy associated with the positive halfcycle of the waveform should equal an energy associated with thenegative half cycle of the waveform. In the embodiment of FIG. 28, theenergy of the positive half cycle 2850 of the first elliptical waveform2810 should be equal to the energy of the negative half cycle 2860 ofthe elliptical waveform 2810 in order to inhibit or prevent sidebands orother signal energy from being created outside of a desired narrowchannel bandwidth. As shown in FIG. 28, each of the elliptical waveformsis of a different maximum and minimum amplitude (A) as a consequence ofthe different zero-crossing points of each elliptical waveform and thebalancing of the energy of the positive and negative half cycles of eachwaveform.

Attention is now directed to FIG. 29, which is a functional blockdiagram of an embodiment of an energy-balancing transmitter 2900configured to generate and transmit zero-crossing-phase-modulatedelliptical waveforms of the type illustrated in FIG. 28. As shown, thetransmitter 2900 includes an input buffer 2904 for storing digital inputdata 2908, a data optimization unit in the form of an AES encryptionmodule 2910, an LDPC coder 2920 and a serial to 4-bit data wordconverter 2930. In one embodiment the transmitter 2900 may beimplemented using, for example, an FPGA.

During operation of the transmitter 2900, input data has been storedwithin the input buffer 2904 is provided to the AES encryption module2910. In one embodiment the AES encryption module 2910 aids in detectionof the data at a receiver by processing the input data to limit the runlength of strings of the same logical value. The resulting outputproduced by the AES encryption module 2910 is provided to the LDPC coder2920, which performs LDPC error correcting coding operations. The serialdata stream produced by the LDPC coder 2920 is then converted into asequence of 4-bit data frames by the serial to 4-bit data word converter2930.

A scale-invariant feature transform table 2940 receives each 4-bit dataword provided by the serial to 4-bit data word converter 2930 andidentifies one of 16 zero-crossing-phase-modulated elliptical waveformsstored therein corresponding to the 4-bit data word. In one embodimentthe table 2940 stores data values (e.g., 3600 data values) correspondingto a single period of each of the 16 zero-crossing-phase-modulatedelliptical waveforms corresponding to each of the 16 possible values ofthe 4-bit data words provided by the data word converter 2930. Inresponse to the sequence of 4-bit data words provided by the data wordconverter 2930, the data values defining each successivezero-crossing-phase-modulated elliptical waveforms are read from thetable 2940 and stored within the wave buffer 2956. For example, inresponse to receipt of the 4-bit digital word [1001], the table 2940 maybe configured to produce, and store within the wave buffer 2956, a setof digital values defining the first elliptical waveform 2810, which hasa zero-crossing phase of 173°.

A time generator 2953 provides a clocking signal to the wave buffer 2956so that a relatively constant data rate is maintained into the filter2960. Since the data rate of the input data provided to the input buffer2904 may be somewhat bursty or otherwise irregular, the time generator2953 functions to essentially remove the resulting jitter from the datastream produced by the scale-invariant feature transform table 2940before it is provided to the filter 2960.

The energy-balanced elliptical waveforms stored within the wave buffer2956 are optionally pre-distorted or otherwise filtered by a filter 2960prior to being converted to analog signals by a digital-to-analogconverter 2964. The resulting encoded analog signals and transmitted viaeither a wired or wireless communication medium.

In one embodiment the transmitter 2900 includes a frequencymonitoring/flow control module 2970 operative to control the data rateinto the scale-invariant feature transform table 2940. Specifically, theflow control module 2970 monitors the data rate out of the dataconverter 2930 and into the wave buffer 2956. When the data rate out ofthe data rate converter 2930 begins to exceed the data rate into thewave buffer 2956, the flow control module 2970 sends 4-bit frames fromthe converter 2930 back to the input buffer 2904 until these data ratesare equalized.

Attention is now directed to FIG. 30, which is a functional blockdiagram of a receiver 3000 configured to receive and demodulatezero-crossing-phase-modulated elliptical waveforms transmitted by atransmitter configured to produce and transmit suchzero-crossing-phase-modulated elliptical waveforms. For example, thereceiver 3000 is capable of receiving and demodulatingzero-crossing-phase-modulated elliptical waveforms transmitted by thetransmitter 2900. As shown, the receiver includes a filter 3010 whichreceives such waveforms, filters extraneous channel noise, and providesthe filtered result to an analog-to-digital converter (ADC) 3020.

A time generator 3024 clocks or otherwise controls the output data rateof the ADC 3020. Digital amplitude values for each received waveform aregenerated by the ADC 3020 and provided to a wave buffer 3028. Once thereceiver 3000 has achieved time synchronization with a receivedelliptical waveform (e.g., by detecting negative-to-positive zerocrossings of the received waveform), the ADC 3020 generates samples ofthe received elliptical waveform at a rate based upon the output of atime generator 3024. The signal samples produced by the ADC 3020 areprovided to a wave buffer 3028.

Once time synchronization with a received waveform has been achieved, adifference measurement module 3030 determines differences betweensamples of a period of the waveform within the wave buffer 3028 andsamples of a sine wave of the same period provided by the time generator3024. In a higher-resolution embodiment such differences are determinedevery 0.1° from 0 to 360° (3600 sample differences per period of thewaveform). In lower-resolution embodiments such differences aredetermined every 1° from 0 to 360° (360 sample differences per period ofthe waveform). The difference measurement module 3030 aggregates thesesample differences for a given period and uses the aggregate differencevalue as an index into a table 3032 that stores a data wordcorresponding to each aggregate difference. For example, in the case inwhich each period of the received elliptical waveform may have one of 16different positive-to-negative zero crossing phases, the table 3032includes a set of 16 4-bit data words corresponding to each of thesezero-crossing phases. That is, each of the aggregated difference valuesis mapped by the table 3032 to one of the 4-bit data words. For example,as shown by the table 3032, one of the aggregate difference values couldcorrespond to a “+1” aggregate difference, which is mapped to a dataword of 0001. Another of the aggregate difference values couldcorrespond to a “−3” aggregate difference, which is mapped to a dataword of 1101, and so on.

In one embodiment sensitivity may be enhanced by configuring the ADC3020 to only operate during certain phase ranges of the receivedelliptical waveforms. In this embodiment, once the receiver 3000 hasachieved time synchronization with a received energy-balanced encodedsine wave, ADC 3020 may be gated “on” so as to only generate samplevalues in the vicinity of the zero crossings proximate the 180° point ofeach period. For example, the ADC 3020 may be turned on only for a timeperiod corresponding to phases spanning the potential zero-crossingphases of interest, e.g., 173° to 187° or slightly wider. Thus, in oneembodiment sensitivity is enhanced by configuring the ADC 3020 to sampleover a relatively small portion of each period.

The data words produced by the measurement module 3030 are provided to adeserializer-to-byte unit 3034, which produces a series of logicalvalues representing the bit values encoded by the zero-crossing phasesof the periods of the received elliptical waveform. The logical valuesgenerated by the byte unit 3034 are then provided to an LDPC decoder3040 configured to remove the LDPC encoding applied by the applicabletransmitter (e.g., the transmitter 2900) from which the receivedelliptical waveform was transmitted. Similarly, an AES decryption unit3046 reverses the encryption applied by a corresponding AES encryptionunit in the applicable transmitter. The output of the AES decryptionunit 3046 may then be provided to an output buffer 3050. In oneembodiment the receiver 3000 searches bit sequences within the outputbuffer 3050 for a preamble data bit string (e.g., a 0x47 string)signifying the start of a packet. In an exemplary implementation theencoded sine waves received by the receiver 3000 carry frames of 1500bits. Each frame begins with a predefined bit string (e.g., 0x47) and isfollowed by the data being communicated. Once the preamble has beenidentified within the output buffer 3050, an estimate of the data beingcommunicated may be provided to a local area network (LAN) or the likevia a network interface 3054. Alternatively, the entire contents of theoutput buffer 3050 may be provided to an external system configured toidentify the preamble for each frame and recover the data conveyed bythe frame.

Referring now to FIG. 31A, there is illustrated a shape-shiftedsinusoidal waveform 3100 encoded using a continuous piecewise functionin accordance with the disclosure. As used herein, the termshape-shifted sinusoidal waveform refers to a generally sinusoidalwaveform that has been shape-shifted over a defined range of phaseangles. In one embodiment a result of this shape-shifting is thatsinusoidal waveforms which have been shape-shifted differently havedifferent zero crossing phases (i.e., are of zero value at differentphases), and hence may be used to define different modulation symbols.In the embodiment of FIG. 31A, the waveform 3100 is illustrative of anyone of a set of generally sinusoidal waveforms having identical periodsbut slightly different shapes. Each symbol waveform, such as theshape-shifted sinusoidal waveform 3100, may uniquely represent a 4-bitdata word corresponding to the zero-crossing phase of the waveform. Inone embodiment each symbol waveform is defined by the followingcontinuous piecewise function Y(θ), where θ represents angulardisplacement and where Y(θ) is continuous between 0 and 2π:

${Y(\theta)} = \begin{pmatrix}{\sin(\theta)} & {{{{0 \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < a} \\{f(\theta)} & {{{{a \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < b} \\{g(\theta)} & {{{{b \leq \theta}\mspace{14mu}\&}\mspace{14mu}\theta} < c} \\{\sin(\theta)} & {c \leq \theta}\end{pmatrix}$

where Y is a value of an encoded waveform comprised of equal periodswhere each symbol waveform occupies one period, θ represents angulardisplacement, and where:

f(x)=sin(π*(θ−d)/(π−2d)),

g(x)=sin(π*(θ+3d)/(π+2d)),

a=π/2,

b=π−d,

c=3π/2.

The parameter d (which may be a positive or negative value) represents aphase shift which defines the zero crossings of each of the symbolwaveforms within their respective periods of the encoded waveform. Thus,each value of d is uniquely associated with a data word, e.g., a 4-bitdata word, corresponding to a particular zero crossing phase of anassociated one of the symbol waveforms. As shown in FIG. 31A, theshape-shifted sinusoidal waveform 3100 crosses zero at a phase θ of π−d.Accordingly, when the symbol waveform 3100 is used to encode 4-bit datawords, a set of sixteen symbol waveforms having different zero crossingphases and identical periods may be employed as modulation symbols,where the value of d associated with each modulation symbol effectivelydefines the zero crossing of such symbol relative to θ=π. For example, afirst symbol waveform 3100 ₁ having a zero-crossing phase of π−d₁ couldrepresent the data word [1001]. A second symbol waveform 3100 ₂ having azero-crossing phase of π−d₂ could, for example, represent the data word[0000], and a third symbol waveform 3100 ₃ having a zero-crossing phaseof π−d₃ could represent the data word [0111].

It has been found that encoded waveforms generated using the function Y,such as the shape-shifted sinusoidal waveform 3100, exhibit little or nosidebands or other signal energy outside of a very narrow channelbandwidth (i.e., on the order of tens or hundreds of Hz depending uponthe period of the encoded waveform).

The function defining Y defining the shape-shifted sinusoidal waveform3100 is advantageously continuous, which may be shown by evaluating thepossible points of discontinuity as follows:

sin(a)=1

f(a)=sin(π*((π/2)−d)/(π−2d))=sin(π*((π)−2d)/2(π−2d))=sin(π/2)=1.

f(b)=sin(π*((π−d)−d)/(π−2d))=sin(π*((π−2d)/(π−2d))=sin(π)=0

g(b)=sin(π*((π−d)+3d)/(π+2d))=sin(π*((π+2d)/(π+2d))=sin(π)=0

g(c)=sin(π*(3π/2+3d)/(π+2d))=sin(3π/2*(π+2d)/(π+2d))=sin(3π/2)=−1

sin(c)=−1.

Since sin(a)=f(a), f(b)=g(b) and g(c)=sin(c), there are no points ofdiscontinuity. Moreover, at the points a and c, the functions f and gattain their maxima are at a slope of 0. At point b, the slope of f(x)is π/(π−2d) and the slope of g(x) is π/(π+2d). Thus, the function Y isalso differentiable at all points except at θ=b.

Turning now to FIG. 31B, there is illustrated a shape-shifted sinusoidalwaveform 3150 alternately encoded using a continuous function inaccordance with the disclosure. The waveform 3150, which is shownrelative to a sine wave 3160, may be shape-shifted to have differentzero crossing phases (i.e., are of zero value at different phases) andhence may be used to define different modulation symbols. In theembodiment of FIG. 31B, the waveform 3150 is illustrative of any one ofa set of generally sinusoidal waveforms having identical periods butslightly different shapes. Each symbol waveform, such as theshape-shifted sinusoidal waveform 3150, may uniquely represent a 4-bitdata word corresponding to the zero-crossing phase of the waveform. Inone embodiment each symbol waveform is defined by the followingcontinuous function y(θ), where θ represents angular displacement:

y(θ)=sin(θ−a(1−cos(θ)))

where

a=½ms·sec(πs/2)².

The parameter s (which may be a positive or negative value) represents aphase shift which defines the zero crossings of each of the symbolwaveforms within their respective periods of the encoded waveform. Thus,each value of s is uniquely associated with a data word, e.g., a 4-bitdata word, corresponding to a particular zero crossing phase of anassociated one of the symbol waveforms. Accordingly, when the symbolwaveform 3150 is used to encode 4-bit data words, a set of sixteensymbol waveforms having different zero crossing phases and identicalperiods may be employed as modulation symbols, where the value of sassociated with each modulation symbol effectively defines the zerocrossing of such symbol relative to 0=n. For example, a first symbolwaveform 3150 ₁ having a zero-crossing phase of π−s₁ could represent thedata word [1001]. A second symbol waveform 3150 ₂ having a zero-crossingphase of π−s₂ could, for example, represent the data word [0000], and athird symbol waveform 3150 ₃ having a zero-crossing phase of π−s₃ couldrepresent the data word [0111].

As may be appreciated by reference to FIG. 31B, a relative phase shift3170 between sine wave 3160 and the phase modulated waveform 3150 peaksaround the value of 0=n and is essentially zero at values of 0=n and0=2n, i.e., at the beginning and end of the symbol period. That is, thephase of waveform 3150 is modulated relative to the sine wave 3160within a period of the encoded waveform, which may be characterized asintra-periodic or sub-periodic phase modulation. It is this adherence bythe sub-periodically modulated waveform 3150 to the phase of the sinewave 3160 at the beginning and the end of each period which is believedto contribute to the extremely narrowband properties of encodedwaveforms comprised of a sequence of phase modulated waveforms 3150.Indeed, it has been found that encoded waveforms generated using thefunction y(θ), such as the shape-shifted sinusoidal waveform 3150,exhibit little or no sidebands or other signal energy outside of a verynarrow channel bandwidth (i.e., on the order of tens or hundreds of Hzdepending upon the period of the encoded waveform).

Attention is now directed to FIG. 32, which is a functional blockdiagram of an embodiment of a transmitter 3200 configured to generateand transmit shape-shifted sinusoidal waveforms of the types illustratedin FIGS. 31A and 31B. As shown, the transmitter 3200 includes an inputbuffer 3204 for storing digital input data 3208, a data optimizationunit in the form of an AES encryption module 3210, an LDPC coder 3220and a serial to 4-bit data word converter 3230. In one embodiment thetransmitter 3200 may be implemented using, for example, an FPGA.

During operation of the transmitter 3200, input data has been storedwithin the input buffer 3204 is provided to the AES encryption module3210. In one embodiment the AES encryption module 3210 aids in detectionof the data at a receiver by processing the input data to limit the runlength of strings of the same logical value. The resulting outputproduced by the AES encryption module 3210 is provided to the LDPC coder3220, which performs LDPC error correcting coding operations. The serialdata stream produced by the LDPC coder 3220 is then converted into asequence of 4-bit data frames by the serial to 4-bit data word converter3230.

In embodiments of the transmitter 3200 designed to transmit the waveform3100 of FIG. 31A, a continuous piecewise function lookup table 3240receives each 4-bit data word provided by the serial to 4-bit data wordconverter 3230 and identifies one of 16 shape-shifted sinusoidalwaveforms stored therein corresponding to the 4-bit data word. In oneembodiment the table 3240 stores data values (e.g., 3600 data values)corresponding to a single period of each of the 16 shape-shiftedsinusoidal waveforms corresponding to each of the 16 possible values ofthe 4-bit data words provided by the data word converter 3230. Inresponse to the sequence of 4-bit data words provided by the data wordconverter 3230, the data values defining each successive shape-shiftedsinusoidal waveform are read from the table 3240 and stored within thewave buffer 3256. For example, in response to receipt of the 4-bitdigital word [1001], the table 3240 may be configured to produce, andstore within the wave buffer 3256, a set of digital values defined byevaluating Y_(n)(θ) between 0 and 2π where the set of digital valuesresult in a zero-crossing phase of π−d_(n).

In embodiments of the transmitter 3200 configured to transmit thewaveform 3150 of FIG. 31B, the lookup table 3240 could be replaced by analternate lookup table storing digital representations of 16shape-shifted sinusoidal waveforms defined by y(θ)=sin(θ−a(1−cos(θ))),where a is defined above.

A time generator 3253 provides a clocking signal to the wave buffer 3256so that a relatively constant data rate is maintained into the filter3260. Since the data rate of the input data provided to the input buffer3204 may be somewhat bursty or otherwise irregular, the time

Continuous waveforms stored within the wave buffer 3256 are optionallypre-distorted or otherwise filtered by a filter 3260 prior to beingconverted to analog signals by a digital-to-analog converter 3264. Theresulting encoded analog signals and transmitted via either a wired orwireless communication medium.

In one embodiment the transmitter 3200 includes a frequencymonitoring/flow control module 3270 operative to control the data rateinto the scale-invariant feature transform table 3240. Specifically, theflow control module 3270 monitors the data rate out of the dataconverter 3230 and into the wave buffer 3256. When the data rate out ofthe data rate converter 3230 begins to exceed the data rate into thewave buffer 3256, the flow control module 3270 sends 4-bit frames fromthe converter 3230 back to the input buffer 3204 until these data ratesare equalized.

Turning now to FIG. 33. a functional block diagram is provided of areceiver 3300 configured to receive and demodulate shape-shiftedsinusoidal continuous piecewise waveforms transmitted by a transmitter.For example, the receiver 3300 is capable of receiving and demodulatingzero-crossing-phase-modulated waveforms transmitted by the transmitter3200 based upon the continuous piecewise function Y(θ) or,alternatively, the continuous function y(θ)=sin(θ−a(1−cos(θ))). Asshown, the receiver includes a filter 3310 which receives suchwaveforms, filters extraneous channel noise, and provides the filteredresult to an analog-to-digital converter (ADC) 3320.

A time generator 3324 clocks or otherwise controls the output data rateof the ADC 3320. Digital amplitude values for each received waveform aregenerated by the ADC 3320 and provided to a wave buffer 3328. Once thereceiver 3300 has achieved time synchronization with a receivedelliptical waveform (e.g., by detecting negative-to-positive zerocrossings of the received waveform), the ADC 3320 generates samples ofthe received elliptical waveform at a rate based upon the output of atime generator 3324. The signal samples produced by the ADC 3320 areprovided to a wave buffer 3328.

Once time synchronization with a received waveform has been achieved, adifference measurement module 3330 determines differences betweensamples of a period of the waveform within the wave buffer 3328 andsamples of a sine wave of the same period provided by the time generator3324. In a higher-resolution embodiment such differences are determinedevery 0.1° from 0 to 360° (3600 sample differences per period of thewaveform). In lower-resolution embodiments such differences aredetermined every 1° from 0 to 360° (360 sample differences per period ofthe waveform). The difference measurement module 3330 aggregates thesesample differences for a given period and uses the aggregate differencevalue as an index into a table 3332 that stores a data wordcorresponding to each aggregate difference.

For example, in the case in which each period of the received waveformmay have one of 16 different positive-to-negative zero crossing phases,the table 3332 includes a set of 16 4-bit data words corresponding toeach of these zero-crossing phases. That is, each of the aggregateddifference values is mapped by the table 3332 to one of the 4-bit datawords. For example, as shown by the table 3332, one of the aggregatedifference values could correspond to a “+1” aggregate difference, whichis mapped to a data word of 0001. Another of the aggregate differencevalues could correspond to a “−3” aggregate difference, which is mappedto a data word of 1101, and so on.

In one embodiment sensitivity may be enhanced by configuring the ADC3320 to only operate during certain phase ranges of the receivedwaveforms. In this embodiment, once the receiver 3300 has achieved timesynchronization with a received waveform, ADC 3320 may be gated “on” soas to only generate sample values in the vicinity of the zero crossingsproximate the 180° point of each period. For example, the ADC 3320 maybe turned on only for a time period corresponding to phases spanning thepotential zero-crossing phases of interest, e.g., 173° to 187° orslightly wider. Thus, in one embodiment sensitivity is enhanced byconfiguring the ADC 3320 to sample over a relatively small portion ofeach period.

The data words produced by the measurement module 3330 are provided to adeserializer-to-byte unit 3334, which produces a series of logicalvalues representing the bit values encoded by the zero-crossing phasesof the periods of the received waveform. The logical values generated bythe byte unit 3334 are then provided to an LDPC decoder 3340 configuredto remove the LDPC encoding applied by the applicable transmitter (e.g.,the transmitter 3200) from which the received continuous piecewisewaveform was transmitted. Similarly, an AES decryption unit 3346reverses the encryption applied by a corresponding AES encryption unitin the applicable transmitter. The output of the AES decryption unit3346 may then be provided to an output buffer 3350. In one embodimentthe receiver 3300 searches bit sequences within the output buffer 3350for a preamble data bit string (e.g., a 0x47 string) signifying thestart of a packet. In an exemplary implementation the encoded waveformsreceived by the receiver 3300 carry frames of 1500 bits. Each framebegins with a predefined bit string (e.g., 0x47) and is followed by thedata being communicated. Once the preamble has been identified withinthe output buffer 3350, an estimate of the data being communicated maybe provided to a local area network (LAN) or the like via a networkinterface 3354. Alternatively, the entire contents of the output buffer3350 may be provided to an external system configured to identify thepreamble for each frame and recover the data conveyed by the frame.

Attention is now directed to FIGS. 34A and 34B, which illustrateshape-shifted sinusoidal waveforms 3400 and 3450 produced by atransmitter configured and in accordance with the disclosure. Theshape-shifted sinusoidal waveforms 3400 and 3450 respectively encode twodifferent binary values (e.g., a 0 and a 1). The shape-shiftedsinusoidal waveforms 3400 and 3450 may be characterized as being of awavelength (referred to herein as λ) and as including two halfwavelengths λ₁ and λ₂ (one higher and one lower than λ) joined at apoint of zero crossing, or “root”. If the bit (b) to be transmitted is a0, then in one embodiment λ₁ will be shorter than λ₂ (see, e.g.,waveform 3400). If a 1 is to be transmitted, then in this embodiment λ₂will be shorter than λ₁ (see, e.g., waveform 3450). It is noted,however, that λ₁+λ₂=λ. The amount by which λ₁ and λ₂ differ from λ iscontrolled by a parameter, hereinafter referred to a s.

In one embodiment the shape-shifted sinusoidal modulation schemed mayalso be characterized by two intermediate parameters, derived from band/or s. The new location of the root is represented by c and thepercent change in the x value of that root is represented by s. As anexample, in a case in which b=1 and s=0.025, the transmittedshape-shifted sinusoidal waveform may be characterized as follows:

b = 1 λ = 1 s = 0.025 u = (2b − 1)s λ₁ = λ(1 + u) λ₂ = λ(1 − u)$c = {\frac{\lambda}{2}\left( {1 + u} \right)}$${T(t)} = \left\{ \begin{matrix}{{{{{{\sin\left( \frac{2{\pi t}}{\lambda_{1}} \right)}0} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < c} \\{{{{{{- {\sin\left( \frac{2{\pi\left( {t - c} \right)}}{\lambda_{2}} \right)}}c} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < \lambda}\end{matrix} \right.$

The values of s of interest in practical applications (e.g., s=0.025)may result in rather subtle changes in shape in the transmittedshape-shifted waveform relative to a pure sinusoid. Accordingly, in theexample of FIGS. 34A and 34B the waveforms 3400 and 3450 were generatedwith a value of s=1 so as to more clearly illustrate differences inshape-shifted sinusoidal waveforms representing a 0 and a 1. In oneembodiment the waveforms FIGS. 34A and 34B could be low-pass filteredprior to transmission so as to remove any noise arising due tonon-differentiability of the waveforms at c (denoted by c₁ in FIG. 34Aand by c₂ in FIG. 34B).

Attention is now directed to FIG. 35, to which reference will be made indescribing an exemplary process for decoding information within areceived shape-shifted shifted sinusoid 3510 encoded in accordance withthe disclosure. The shape-shifted shifted sinusoid 3510 represents ashape-shifted shifted sinusoid generated and transmitted by atransmitter and received by a receiver. As shown, a first integrationinterval 3520 and a second integration interval 3530 are definedrelative to the shape-shifted sinusoid 3510. In one embodiment edges ofthese intervals occur at a predefined number of degrees (e.g., ±15degrees) from the roots 3540, or zero crossings, of a pure sine wave ofwavelength k. Within the receiver a comparison is made of the twointegrals of the squares of the amplitude of the shape-shifted shiftedsinusoid 3510 across the two intervals 3510 and 3520. This may, forexample, involve computing the sum of the squares of samples of theshape-shifted shifted sinusoid 3510 across the intervals 3510 and 3520.If the value of the integral computed over the first integrationinterval 3510 is larger than the integral value computed over the secondintegration interval 3520, it is inferred that a one (1) wastransmitted, i.e., λ₂ shorter than λ₁, and that otherwise a zero wastransmitted. In the example of FIG. 35, the shape-shifted shiftedsinusoid 3510 has been synthesized to encode a one (1) using a value ofs (i.e., s=2.5%) suitable for a practical application.

The disclosure discussed herein provides and describes examples of someembodiments of the system for data communication with high spectralefficiency. The designs, figures, and descriptions are non-limitingexamples of selected embodiments of the disclosure. For example, otherembodiments of the disclosed device may or may not include the featuresdescribed herein. Moreover, disclosed advantages and benefits may applyto only certain embodiments of the disclosure and should not be used tolimit the various disclosures.

As used herein, coupled means directly or indirectly connected by asuitable means known to persons of ordinary skill in the art. Coupleditems may include interposed features such as, for example, A is coupledto C via B. Unless otherwise stated, the type of coupling, whether it bemechanical, electrical, fluid, optical, radiation, or other is indicatedby the context in which the term is used.

As used in this specification, a module can be, for example, anyassembly and/or set of operatively-coupled electrical componentsassociated with performing a specific function(s), and can include, forexample, a memory, a processor, electrical traces, optical connectors,software (that is stored in memory and/or executing in hardware) and/orthe like.

As used in this specification, the singular forms “a,” “an” and “the”include plural referents unless the context clearly dictates otherwise.Thus, for example, the term “an actuator” is intended to mean a singleactuator or a combination of actuators.

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not of limitation. Likewise, the various diagrams maydepict an example architectural or other configuration for theinvention, which is done to aid in understanding the features andfunctionality that can be included in the invention. The invention isnot restricted to the illustrated example architectures orconfigurations, but can be implemented using a variety of alternativearchitectures and configurations. Additionally, although the inventionis described above in terms of various embodiments and implementations,it should be understood that the various features and functionalitydescribed in one or more of the individual embodiments are not limitedin their applicability to the particular embodiment with which they aredescribed, but instead can be applied, alone or in some combination, toone or more of the other embodiments of the invention, whether or notsuch embodiments are described and whether or not such features arepresented as being a part of a described embodiment. Thus the breadthand scope of the present invention should not be limited by any of theabove-described embodiments.

Some embodiments described herein relate to a computer storage productwith a non-transitory computer-readable medium (also can be referred toas a non-transitory processor-readable medium) having instructions orcomputer code thereon for performing various computer-implementedoperations. The computer-readable medium (or processor-readable medium)is non-transitory in the sense that it does not include transitorypropagating signals per se (e.g., a propagating electromagnetic wavecarrying information on a transmission medium such as space or a cable).The media and computer code (also can be referred to as code) may bethose designed and constructed for the specific purpose or purposes.Examples of non-transitory computer-readable media in which the KCM mayreside include, without limitation, one time programmable (OTP) memory,protected Random-Access Memory (RAM) and flash memory.

Examples of computer code include, but are not limited to, micro-code ormicro-instructions, machine instructions, such as produced by acompiler, code used to produce a web service, and files containinghigher-level instructions that are executed by a computer using aninterpreter. For example, embodiments may be implemented usingimperative programming languages (e.g., C, Fortran, etc.), functionalprogramming languages (Haskell, Erlang, etc.), logical programminglanguages (e.g., Prolog), object-oriented programming languages (e.g.,Java, C++, etc.) or other suitable programming languages and/ordevelopment tools. Additional examples of computer code include, but arenot limited to, control signals, encrypted code, and compressed code.

While various embodiments have been described above, it should beunderstood that they have been presented by way of example only, and notlimitation. Where methods described above indicate certain eventsoccurring in certain order, the ordering of certain events may bemodified. Additionally, certain of the events may be performedconcurrently in a parallel process when possible, as well as performedsequentially as described above. Although various modules in thedifferent devices are shown to be located in the processors of thedevice, they can also be located/stored in the memory of the device(e.g., software modules) and can be accessed and executed by theprocessors. Accordingly, the specification is intended to embrace allsuch modifications and variations of the disclosed embodiments that fallwithin the spirit and scope of the appended claims.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of.” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

1-15. (canceled)
 16. A data communication method, the method comprising: receiving input digital data; encoding the input digital data into an encoded waveform having zero crossings representative of the input digital data, the encoding including generating each period of the encoded waveform using a continuous function y(Θ), where y(Θ) given by: y(Θ)=sin(Θ−a(1−cos(Θ))) where a=½πs·sec(πs/2)² wherein s represents a phase shift; and generating an encoded analog waveform from a representation of the encoded waveform.
 17. The method of claim 16 wherein the encoding the input digital data uses a plurality of symbol waveforms and wherein each of the plurality of symbol waveforms occupies a period of the encoded waveform and represents at least one bit of the input digital data.
 18. The method of claim 17 wherein the plurality of symbol waveforms are defined so that a value of s is different for each of the plurality of symbol waveforms.
 19. The method of claim 17, further including: storing digital representations of the plurality of symbol waveforms within a memory; reading out ones of the digital representations from the memory upon the receiving of the input digital data.
 20. The method of claim 17 wherein a period of each symbol waveform is equal.
 21. The method of claim 17 wherein the input digital data includes a plurality of data words of at least four bits, the plurality of symbol waveforms respectively corresponding to the plurality of data words.
 22. A method of recovering input digital data encoded by symbol waveforms wherein each of the symbol waveforms occupies a period of an encoded waveform and wherein each period of the encoded waveform is generated using a continuous function y(Θ), where y(Θ) given by: y(Θ)=sin(Θ−a(1−cos(Θ))) where a=½πs·sec(πs/2)² wherein s represents a phase shift, the method including: receiving an encoded analog waveform generated using the encoded waveform; generating digital symbol samples representing the symbol waveforms included within the encoded waveform; identifying a first sample of the digital symbol samples corresponding to a transition in polarity of the digital symbol samples from a first polarity to a second polarity; determining a second sample of the digital signal samples corresponding to a transition from other ones of the digital signal samples of the second polarity to other ones of the digital signal samples of the first polarity; and estimating the input digital data based upon the first sample and the second sample.
 23. The method of claim 22 wherein the estimating includes estimating a zero crossing value based upon the first sample and the second sample, the zero crossing value being included among a plurality of zero crossing values, each of the plurality of zero crossing values corresponding to a different digital data word.
 24. The method of claim 22 wherein the estimating includes determining a number of samples between the first sample and the second sample.
 25. A system, comprising: an input buffer configured to store input digital data; a time domain modulator for encoding the input digital data into an encoded waveform having zero crossings representative of the input digital data, the time domain modulator generating each period of the encoded waveform using a continuous function y(Θ), where y(Θ) given by: y(Θ)=sin(Θ−a(1−cos(Θ))) where a=½πs·sec(πs/2)² wherein s represents a phase shift; and one or more digital-to-analog converters for generating an encoded analog waveform from a representation of the encoded waveform.
 26. The system of claim 25 wherein the time domain modulator uses a plurality of symbol waveforms to encode the input digital data and wherein each of the plurality of symbol waveforms occupies a period of the encoded waveform and represents at least one bit of the input digital data.
 27. The system of claim 26 wherein each symbol waveform is defined so that a zero crossing within the period of the encoded waveform occupied by the symbol waveform is different from the zero crossing within periods of the encoded waveform occupied by other of the plurality of symbol waveforms.
 28. The system of claim 26, further including a memory configured to store digital representations of the plurality of symbol waveforms wherein the time domain modulator is configured to read out ones of the digital representations from the memory upon the receiving of the input digital data.
 29. The system of claim 26 wherein a period of each symbol waveform is equal.
 30. The system of claim 26 wherein the input digital data includes a plurality of data words of at least four bits, the plurality of symbol waveforms respectively corresponding to the plurality of data words.
 31. A data communication method, the method comprising: receiving input digital data; encoding the input digital data into an encoded waveform representative of the input digital data wherein the encoded waveform is of a wavelength λ and wherein each period of the encoded waveform includes a first half sinusoid corresponding to one half of a first sinusoid of wavelength λ₁ and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ2, where λ₁+λ₂=λ, the encoding including generating each period of the encoded waveform so as to represent one bit of the input digital data; wherein the first half sinusoid is of a first polarity and the second half sinusoid of a second polarity opposite to the first polarity; wherein a first bit value of the input digital data is represented when λ₁ is greater than λ₂ and a second bit value of the input digital data is represented when λ₂ is greater than λ₁; and generating an encoded analog waveform from a representation of the encoded waveform.
 32. The data communication method of claim 31 wherein each period of the encoded waveform is represented by a function T(t), where T(t) is given by: ${T(t)} = \left\{ {{\begin{matrix} {{{{{{\sin\left( \frac{2{\pi t}}{\lambda_{1}} \right)}0} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < c} \\ {{{{{{- {\sin\left( \frac{2{\pi\left( {t - c} \right)}}{\lambda_{2}} \right)}}c} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < \lambda} \end{matrix}{where}c} = {{\frac{\lambda}{2}\left( {1 + u} \right)u} = {{\left( {{2b} - 1} \right)s\lambda_{1}} = {{{\lambda\left( {1 + u} \right)}\lambda_{2}} = {\lambda\left( {1 - u} \right)}}}}} \right.$ wherein b represents a value of the input digital data being encoded, c is a root location joining the first half sinusoid and the second half sinusoid, and s represents a change between the root location and a default root location corresponding to λ₁=λ₂.
 33. A method of recovering input digital data encoded into an encoded waveform of a wavelength λ wherein each period of the encoded waveform includes a first half sinusoid corresponding to one half of a first sinusoid of wavelength λ₁ and a second half sinusoid corresponding to one half of a second sinusoid of wavelength λ₂, where λ₁+λ₂=λ, the encoding including generating each period of the encoded waveform so as to represent one bit of the input digital data; wherein the first half sinusoid is of a first polarity and the second half sinusoid of a second polarity opposite to the first polarity; wherein a first bit value is represented when λ₁ is greater than λ₂ and a second bit value is represented when λ₂ is greater than λ₁; the method including: receiving an encoded analog waveform generated using the encoded waveform; generating digital symbol samples representing the first half sinusoid and the second half sinusoid of a first period of the encoded waveform; computing a first sum of squares of the digital symbol samples over a first integration interval encompassed by the first half sinusoid; computing a second sum of squares of the digital symbol samples over a second integration interval encompassed by the second half sinusoid; estimating a bit of the input digital data encoded by a first period of the encoded waveform based upon a comparison of the first sum of squares and the second sum of squares.
 34. The method of claim 33 further including, for each period of the encoded waveform following the first period: generating digital symbol samples representing the first half sinusoid and the second half sinusoid for the period of the encoded waveform; computing a first sum of squares of the digital symbol samples over a first integration interval encompassed by the first half sinusoid; computing a second sum of squares of the digital symbol samples over a second integration interval encompassed by the second half sinusoid; estimating a bit of the input digital data encoded by the period of the encoded waveform based upon a comparison of the first sum of squares and the second sum of squares.
 35. The method of claim 33 wherein a first edge of the first integration interval is located a predefined number of degrees before a zero crossing of a sine wave of wavelength λ and wherein a first edge of the second integration interval is located the predefined number of degrees after the zero crossing.
 36. The method of claim 33 wherein each period of the encoded waveform is represented by a function T(t), where T(t) is given by: ${T(t)} = \left\{ {{\begin{matrix} {{{{{{\sin\left( \frac{2{\pi t}}{\lambda_{1}} \right)}0} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < c} \\ {{{{{{- {\sin\left( \frac{2{\pi\left( {t - c} \right)}}{\lambda_{2}} \right)}}c} \leq t}\mspace{14mu}\&}\mspace{14mu} t} < \lambda} \end{matrix}{where}c} = {{\frac{\lambda}{2}\left( {1 + u} \right)u} = {{\left( {{2b} - 1} \right)s\lambda_{1}} = {{{\lambda\left( {1 + u} \right)}\lambda_{2}} = {\lambda\left( {1 - u} \right)}}}}} \right.$ wherein b represents a value of the input digital data being encoded, c is a root location joining the first half sinusoid and the second half sinusoid, and s represents a change between the root location and a default root location corresponding to λ₁=λ₂. 